The word rati is explained in the Bhakti-rasāmṛta-sindhu (1.3.41) as follows:
vyaktaṁ masṛṇatevāntar-lakṣyate rati-lakṣaṇam
mumukṣu-prabhṛtīnāṁ ced bhaved eṣā ratir na hi
"When a tenderness of the heart is manifested, there is rati, or attachment. But those who are interested in being liberated from material bondage will not manifest this tenderness." This attachment is not like material attachment. When one is free of material contamination, attachment for Kṛṣṇa's service awakens and is called rati. In the material world there is attachment for material enjoyment, but this is not rati. Transcendental rati can be awakened only on the spiritual platform. Ecstatic love for Kṛṣṇa (prema) is described in the Bhakti-rasāmṛta-sindhu(1.41) as follows:

samyaṅ masṛṇita-svānto mamatvātiśayāṅkitaḥ
bhāvaḥ sa eva sāndrātmā budhaiḥ premā nigadyate
“When the heart is completely softened and devoid of all material desires and when one's emotional feelings become very strong, one becomes very much attached to Kṛṣṇa. Such purified emotion is known as pure love.”

(Sri Caitanya Caritamrta-----2:19:177-----purport).

In the Bhakti-rasāmṛta-sindhu, (3.2.84) sneha (affection) is described as follows:
sāndraś citta-dravaṁ kurvan premā "sneha" itīryate

kṣaṇikasyāpi neha syād viśleṣasya sahiṣṇutā
"That aspect of prema in which the melting of the heart for the lover is concentrated is called sneha, or affection. The symptom of such affection is that the lover cannot for a moment remain without the association of the beloved." A description of māna can be found in Madhya-līlā (Chapter Two, verse 66). Similarly, a description of praṇaya is also there. As far as rāga is concerned, the Bhakti-rasāmṛta-sindhu (3.2.87) says:

snehaḥ sa rāgo yena syāt sukhaṁ duḥkham api sphuṭam
tat-sambandha-lave ‘py atra prītiḥ prāṇa-vyayair api
"That stage at which affection for the beloved converts unhappiness into happiness is called rāga, or attachment. When one has such attachment for Kṛṣṇa, he can give up his own life to satisfy his beloved Kṛṣṇa." Anurāga, bhāva and mahābhāva are described in the Sixth Chapter of the Madhya-līlā, verse 13. The purport to that verse explains adhirūḍha-mahābhāva.

(Sri Caitanya Caritamrta-----2:19:178-----purport).

Attachment for Kṛṣṇa never wanes; it increases more and more as one attains different stages. All the stages together are called sthāyibhāva, or continuous existence of ecstasy. The nine forms of devotional service are śravaṇaṁ kīrtanaṁ viṣṇoḥ smaraṇaṁ pāda-sevanam arcanaṁ vandanaṁ dāsyaṁ sakhyam ātma-nivedanam (S.B.7:5:23). When continuous love of Godhead is mixed with the processes of devotional service, it is called vibhāva, anubhāva, sāttvika and vyabhicārī. The devotee thus enjoys a variety of transcendental bliss. In his Amṛta-pravāha-bhāṣya, Śrīla Bhaktivinoda Ṭhākura states that anubhāva can be divided into thirteen categories: (1) dancing, (2) rolling on the ground, (3) singing, (4) yelling, (5) jumping, (6) making loud noises, (7) yawning, (8) heavy breathing, (9) not caring for public opinion, (10) discharging saliva, (11) roaring laughter, (12) unsteadiness and (13) hiccuping. These are the symptoms of anubhāva. Thus the transcendental mellows are experienced in different stages. Similarly, there are many other forms of expression that have been analytically studied by the Gosvāmīs. In the Bhakti-rasāmṛta-sindhu, Rūpa Gosvāmī gives each and every symptom a particular name.

(Sri Caitanya Caritamrta-----2:19:180-----purport).

Śānta-rati is described in the Bhakti-rasāmṛta-sindhu (2.5.16–18) as follows:
mānase nirvikalpatvaṁ
śama ity abhidhīyate
"When one is completely free from all doubts and material attachments, he attains the neutral position, called śānta."

vihāya viṣayonmukhyaṁ nijānanda-sthitir yataḥ
ātmanaḥ kathyate so ’tra svabhāvaḥ śama ity asau
prāyaḥ śama-pradhānānāṁ mamatā-gandha-varjitā
paramātmatayā kṛṣṇe jātā śāntī ratir matā
The śānta-rati realization of Kṛṣṇa is in the neutral stage between the conception of impersonalism and personalism. This means that one is not very strongly attached to the personal feature of the Lord. An appreciation of the greatness of the Lord is called śānta-rati. This is attachment not to the personal feature but to the impersonal feature. Generally, one in this stage is attached to the Paramātmā feature of the Supreme Personality of Godhead.

(Sri Caitanya Caritamrta-----2:19:183-184-----purport).

“The Supreme Lord is situated in everyone's heart, O Arjuna, and is directing the wanderings of all living entities, who are seated as on a machine made of the material energy.” (B.G.18:61) On the strength of this statement from the Bhagavad-gītā, we can understand that in śānta-rasa a devotee sees the Lord's representation everywhere.
Dāsya-rati is explained in the Bhakti-rasāmṛta-sindhu (2.5.27) thus:

svasmād bhavanti ye nyūnās te ’nugrāhyā harer matāḥ
ārādhyatvātmikā teṣāṁ ratiḥ prītir itīritā
tatrāsakti-kṛd anyatra prīti-saṁhāriṇī hy asau
When the Supreme Lord in His localized aspect is appreciated and a great devotee understands his subordinate position, not only does he surrender to the Supreme Personality of Godhead, but, due to his subordinate position, he wishes to render some service and thus become favored by the Supreme Personality of Godhead.

(Sri Caitanya Caritamrta-----2:19:183-184-----purport).

Vātsalya-rati is described as follows in the Bhakti-rasāmṛta-sindhu (2.5.33):
guravo ye harer asya te pūjyā iti viśrutāḥ
anugraha-mayī teṣāṁ ratir vātsalyam ucyate
idaṁ lālana-bhavyāśīś cibuka-sparśanādi-kṛt
When a living entity is situated on the platform of vātsalya-rati, he thinks of the Supreme Personality of Godhead in His childhood feature. In this feature, the Lord has to be protected by the devotee, and at this time the devotee takes the position of being worshiped by the Supreme Personality of Godhead. These feelings of parental love are called vātsalya-rati. When the devotee is situated on this platform, he wants to maintain the Lord like a son, and he desires all good fortune for the Lord. He offers blessings to the Lord by touching His feet and head.

(Sri Caitanya Caritamrta-----2:19:183-184-----purport).

Śānta-bhakti-rasa is described in the Bhakti-rasāmṛta-sindhu (3.1.4–6) as follows:
vakṣyamāṇair vibhāvādyaiḥ śamināṁ svādyatāṁ gataḥ
sthāyī śānti-ratir dhīraiḥ śānta-bhakti-rasaḥ smṛtaḥ
prāyaḥ sva-sukha-jātīyaṁ sukhaṁ syād atra yoginām
kintv ātma-saukhyam aghanaṁ ghanaṁ tv īśa-mayaṁ sukham
tatrāpīśa-svarūpānubhavasyaivoru-hetutā
dāsādi-van-mano-jñātva-līlāder na tathā matā
When śānta-rati (neutral attraction) exists continuously and is mixed with ecstatic emotion, and when the devotee relishes that neutral position, it is called śānta-bhakti-rasa. Śānta-bhakti-rasa devotees generally relish the impersonal feature of the Supreme Personality of Godhead. Since their taste of transcendental bliss is incomplete, it is called aghana, or not concentrated.

(Sri Caitanya Caritamrta-----2:19:185-----purport).

Dāsya-rasa, or dāsya-bhakti-rasa, is described in the Bhakti-rasāmṛta-sindhu (3.2.3–4) as follows:
ātmocitair vibhāvādyaiḥ prītir āsvādanīyatām
nītā cetasi bhaktānāṁ prīti-bhakti-raso mataḥ
anugrāhy asya dāsatvāl lālyatvād apy ayaṁ dvidhā
bhidyate sambhrama-prīto gaurava-prīta ity api
When according to his desires the living entity develops love for the Supreme Personality of Godhead, this beginning stage of love is called dāsya-bhakti-rasa. Dāsya-bhakti-rasa is divided into two categories, called sambhrama-dāsya and gaurava-dāsya. In sambhrama-dāsya, the devotee renders respectful service to the Supreme Personality of Godhead, but in the more advanced gaurava-dāsya, the devotee feels that he is receiving protection from the Lord.

(Sri Caitanya Caritamrta-----2:19:185-----purport).

Sakhya-bhakti-rasa is described as follows in the Bhakti-rasāmṛta sindhu (3.3.1):
sthāyi-bhāvo vibhāvādyaiḥ sakhyam ātmocitair iha
nītaś citte satāṁ puṣṭiṁ rasaḥ preyān udīryate
“According to one's original consciousness, ecstatic emotions may be exhibited as continuously existing in fraternity. When this stage of Kṛṣṇa consciousness is mature, it is called preyo-rasa or sakhya-bhakti-rasa.”

Vātsalya-bhakti-rasa is described in the Bhakti-rasāmṛta-sindhu (3.4.1) as follows:

vibhāvādyais tu vātsalyaṁ sthāyī puṣṭim upāgataḥ
eṣa vatsala-nāmātra prokto bhakti-raso budhaiḥ
"When eternally existing love of Godhead transforms into parental love and is mixed with corresponding emotions, that stage of spiritual existence is described by learned devotees as vātsalya-bhakti-rasa."

(Sri Caitanya Caritamrta-----2:19:185-----purport).

Madhura-bhakti-rasa is described in the Bhakti-rasāmṛta-sindhu (3.5.1) as follows:
ātmocitair vibhāvādyaiḥ puṣṭiṁ nītā satāṁ hṛdi
madhurākhyo bhaved bhakti-raso ‘sau madhurā ratiḥ
“If in accordance with one's own natural development in Kṛṣṇa consciousness one's attraction leans toward conjugal love within the heart, that is called attachment in conjugal love, or madhura-rasa.”

(Sri Caitanya Caritamrta-----2:19:185-----purport).