Kṛṣṇa is the original Supreme Personality of Godhead, and Baladeva is Kṛṣṇa's immediate expansion. Both Lord Kṛṣṇa and Baladeva appeared as sons of Vasudeva, so both of Them may be called Vāsudeva. From another point of view, because Kṛṣṇa never leaves Vṛndāvana, all the forms of Kṛṣṇa that appear elsewhere are His expansions. Vāsudeva is Kṛṣṇa's immediate expansion, so Vāsudeva is not different from Kṛṣṇa. It is to be understood that the Vāsudeva referred to in this verse of Bhagavad-gītā is Baladeva, or Balarāma, because He is the original source of all incarnations and thus He is the sole source of Vāsudeva. The immediate expansions of the Lord are called svāṁśa (personal expansions), and there are also expansions called vibhinnāṁśa (separated expansions).
(Bhagavad-Gita-----10:37-----purport).

The speciality of devotional service unto the Personality of Godhead Lord Śrī Kṛṣṇa is specifically mentioned herein. Lord Śrī Kṛṣṇa is the svayaṁ-rūpa Personality of Godhead, and all other forms of Godhead, beginning from Śrī Baladeva, Saṅkarṣaṇa, Vāsudeva, Aniruddha, Pradyumna and Nārāyaṇa and extending to the puruṣa-avatāras, guṇa-avatāras, līlā-avatāras, yuga-avatāras and many other thousands of manifestations of the Personality of Godhead, are Lord Śrī Kṛṣṇa's plenary portions and integrated parts. The living entities are separated parts and parcels of the Personality of Godhead. Therefore Lord Sri Kṛṣṇa is the original form of Godhead, and He is the last word in the Transcendence. Thus He is more attractive to the higher transcendentalists who participate in the eternal pastimes of the Lord.
(Srimad Bhagavatam-----1:2:22-----purport).

Baladeva: He is the divine son of Vasudeva by his wife Rohiṇī. He is also known as Rohiṇī-nandana, the beloved son of Rohiṇī. He was also entrusted to Nanda Mahārāja along with His mother, Rohiṇī, when Vasudeva embraced imprisonment by mutual agreement with Kaṁsa. So Nanda Mahārāja is also the foster father of Baladeva along with Lord Kṛṣṇa. Lord Kṛṣṇa and Lord Baladeva were constant companions from Their very childhood, although They were stepbrothers. He is the plenary manifestation of the Supreme Personality of Godhead, and therefore He is as good and powerful as Lord Kṛṣṇa. He belongs to the viṣṇu-tattva (the principle of Godhead). He attended the svayaṁvara ceremony of Draupadī along with Śrī Kṛṣṇa. When Subhadrā was kidnapped by Arjuna by the organized plan of Śrī Kṛṣṇa, Baladeva was very angry with Arjuna and wanted to kill him at once. Śrī Kṛṣṇa, for the sake of His dear friend, fell at the feet of Lord Baladeva and implored Him not to be so angry. Śrī Baladeva was thus satisfied. Similarly, He was once very angry with the Kauravas, and He wanted to throw their whole city into the depths of the Yamunā. But the Kauravas satisfied Him by surrendering unto His divine lotus feet. He was actually the seventh son of Devakī prior to the birth of Lord Kṛṣṇa, but by the will of the Lord He was transferred to the womb of Rohiṇī to escape the wrath of Kaṁsa. His other name is therefore Saṅkarṣaṇa, who is also the plenary portion of Śrī Baladeva. Because He is as powerful as Lord Kṛṣṇa and can bestow spiritual power to the devotees, He is therefore known as Baladeva. In the Vedas also it is enjoined that no one can know the Supreme Lord without being favored by Baladeva. Bala means spiritual strength not physical. Some less intelligent persons interpret bala as the strength of the body. But no one can have spiritual realization by physical strength. Physical strength ends with the end of the physical body, but spiritual strength follows the spirit soul to the next transmigration, and therefore the strength obtained by Baladeva is never wasted. The strength is eternal, and thus Baladeva is the original spiritual master of all devotees.
(Srimad Bhagavatam-----1:11:16-17-----purport).

Śrī Baladeva was also a class friend of Lord Śrī Kṛṣṇa as a student of Sāndīpani Muni. In His childhood He killed many asuras along with Śrī Kṛṣṇa, and specifically He killed the Dhenukāsura at Tālavana. During the Kurukṣetra battle, He remained neutral, and He tried His best not to bring about the fight. He was in favor of Duryodhana, but still He remained neutral. When there was a club-fight between Duryodhana and Bhīmasena, He was present on the spot. He was angry at Bhīmasena when the latter struck Duryodhana on the thigh or below the belt, and He wanted to retaliate the unfair action. Lord Śrī Kṛṣṇa saved Bhīma from His wrath. But He left the place at once, being disgusted at Bhīmasena, and after His departure Duryodhana fell to the ground to meet his death. The funeral ceremony of Abhimanyu, the son of Arjuna, was performed by Him, as He was the maternal uncle. It was impossible to be performed by any one of the Pāṇḍavas, who were all overwhelmed with grief. At the last stage, He departed from this world by producing a great white snake from His mouth, and thus He was carried by Śeṣanāga in the shape of a serpent.
(Srimad Bhagavatam-----1:11:16-17-----purport).

Hastināpura, the capital of the Pāṇḍavas, was situated somewhere near present New Delhi, and the kingdom of Ugrasena was situated in Mathurā. While returning to Delhi from Dvārakā, Arjuna must have visited the city of Mathurā, and therefore the inquiry about the King of Mathurā is valid. Amongst various names of the relatives, the name of Rāma or Balarāma, eldest brother of Lord Kṛṣṇa, is added with the words "the Personality of Godhead" because Lord Balarāma is the immediate expansion of viṣṇu-tattva as prakāśa-vigraha of Lord Kṛṣṇa. The Supreme Lord, although one without a second, expands Himself as many other living beings. The viṣṇu-tattva living beings are expansions of the Supreme Lord, and all of them are qualitatively and quantitatively equal with the Lord. But expansions of the jīva-śakti, the category of the ordinary living beings, are not at all equal with the Lord.
(Srimad Bhagavatam-----1:14:28:29-----purport).

One who considers the jīva-śakti and the viṣṇu-tattva to be on an equal level is considered a condemned soul of the world. Śrī Rāma, or Balarāma, is the protector of the devotees of the Lord. Baladeva acts as the spiritual master of all devotees, and by His causeless mercy the fallen souls are delivered. Śrī Baladeva appeared as Śrī Nityānanda Prabhu during the advent of Lord Caitanya, and the great Lord Nityānanda Prabhu exhibited His causeless mercy by delivering a pair of extremely fallen souls, namely Jagāi and Mādhāi. Therefore it is particularly mentioned herein that Balarāma is the protector of the devotees of the Lord. By His divine grace only one can approach the Supreme Lord Śrī Kṛṣṇa, and thus Śrī Balarāma is the mercy incarnation of the Lord, manifested as the spiritual master, the savior of the pure devotees.
(Srimad Bhagavatam-----1:14:28:29-----purport).

In the Viṣṇu Purāṇa, as well as in the Mahābhārata, both Kṛṣṇa and Baladeva are mentioned as having beautiful black hair, even in Their advanced age. The Lord is called anupalakṣya-mārgaḥ or, in still more technical Vedic terms, avāṅ-manasā gocaraḥ: one who is never to be seen or realized by the limited sense perception of the people in general. In the Bhagavad-gītā (7.25) it is said by the Lord, nāhaṁ prakāśaḥ sarvasya yogamāyā-samāvṛtaḥ. In other words, He reserves the right of not being exposed to anyone and everyone. Only the bona fide devotees can know Him by His specific symptoms, and out of many, many such symptoms, one symptom is mentioned here in this verse, that the Lord is sita-kṛṣṇa-keśaḥ, or one who is observed always with beautiful black hair.
(Srimad Bhagavatam-----2:7:26-----purport).

Lord Kṛṣṇa and Balarāma are not two different Personalities of Godhead. God is one without a second, but He expands Himself in many forms without their being separate from one another. They are all plenary expansions. The immediate expansion of Lord Kṛṣṇa is Baladeva, and Brahmā, born from the lotus flower from Garbhodakaśāyī Viṣṇu, is an expansion of Baladeva. This indicates that Kṛṣṇa and Baladeva are not subjected to the regulations of the universe; on the contrary, the whole universe is under Their subjugation. They appeared at the request of Brahmā to liberate the burden of the world, and They relieved the world by many superhuman activities so that everyone became happy and prosperous.
(Srimad Bhagavatam-----3:1:26-----purport).

The śāstras say everywhere that Kṛṣṇa is the original Personality of Godhead and that He has innumerable avatāras, or incarnations. Elsewhere in the Brahma-saṁhitā it is said, rāmādi-mūrtiṣu kalā-niyamena tiṣṭhan: (Bs. 5.39) Rāma, Nṛsiṁha, Varāha and many others are consecutive expansions of the Supreme Personality of Godhead. After Kṛṣṇa comes Balarāma, after Balarāma is Saṅkarṣaṇa, then Aniruddha, Pradyumna, Nārāyaṇa and then the puruṣa-avatāras—Mahā-Viṣṇu, Garbhodakaśāyī Viṣṇu and Kṣīrodakaśāyī Viṣṇu. All of them are avatāras.
(Srimad Bhagavatam-----7:10:42-----purport).

Significant in this verse are the words jñānāsim acyuta-balaḥ. Jñānāsim, the sword of knowledge, is given by Kṛṣṇa, and when one serves the guru and Kṛṣṇa in order to hold the sword of Kṛṣṇa's instructions, Balarāma gives one strength. Balarāma is Nityānanda. Vrajendra-nandana yei, śacī-suta haila sei, balarāma ha-ila nitāi. This bala—Balarāma—comes with Śrī Caitanya Mahāprabhu, and both of Them are so merciful that in this age of Kali one may very easily take shelter of Their lotus feet. They come especially to deliver the fallen souls of this age. pāpī tāpī yata chila, hari-nāme uddhārila. Their weapon is saṅkīrtana, hari-nāma. Thus one should accept the sword of knowledge from Kṛṣṇa and be strong with the mercy of Balarāma. We are therefore worshiping Kṛṣṇa-Balarāma in Vṛndāvana.
(Srimad Bhagavatam-----7:15:45-----purport).

In the Muṇḍaka Upaniṣad (3.2.4) it is said:
nāyam ātmā bala-hīnena labhyo
na ca pramādāt tapaso vāpy aliṅgāt
etair upāyair yatate yas tu vidvāṁs
tasyaiṣa ātmā viśate brahma-dhāma
One cannot attain the goal of life without the mercy of Balarāma. Śrī Narottama dāsa Ṭhākura therefore says, nitāiyera karuṇā habe, vraje rādhā-kṛṣṇa pābe: when one receives the mercy of Balarāma, Nityānanda, one can attain the lotus feet of Rādhā and Kṛṣṇa very easily.
se sambandha nāhi yāra, bṛthā janma gela tāra,
vidyā-kule hi karibe tāra
If one has no connection with Nitāi, Balarāma, then even though one is a very learned scholar or jñānī or has taken birth in a very respectable family, these assets will not help him. We must therefore conquer the enemies of Kṛṣṇa consciousness with the strength received from Balarāma.
(Srimad Bhagavatam-----7:15:45-----purport).