Quoting from Wikipedia about the avtaars Vishnu. They differ acc. to the Sources:
The ten best known avatars of Vishnu are collectively known as the Dasavatara ("ten avatars"). This list is included in the Garuda Purana (1.86.10"11).
The first four are said to have appeared in the Satya Yuga (the first of the four Yugas or ages in the time cycle described within Hinduism). The next three avatars appeared in the Treta Yuga, the eighth descent in the Dwapara Yuga and the ninth in the Kali Yuga. The tenth, Kalki, is predicted to appear at the end of the Kali Yuga.
Matsya, the fish-avatar who saved Manu - the progeniter of mankind from the great deluge and rescued the Vedic scriptures by killing a demon. Story can be found in the Matsya Purana.
Kurma, the tortoise-avatar, who helped in the Samudra manthan - the churning of the ocean. Story can be found in the Kurma Purana.
Varaha, the boar-avatar, who rescued the earth from the ocean, by killing her kidnapper-demon Hiranyaksha. Story can be found in the Varaha Purana.
Narasimha, the half man-half lion avatar, who killed the tyrant demon-king Hiranyakashipu, to rescue the demon's son Prahlada, who was a Vishnu-devotee.
Vamana, the dwarf-avatar, who subdued the king Maha Bali. Story can be found in the Vamana Purana.
Parashurama, sage with the axe who killed the thousand-armed king Kartavirya Arjuna.
Rama, the king of Ayodhya and the hero of the Hindu epic Ramayana.
Krishna, the king of Dwarka, a central character in the Bhagavata Purana and the Mahabharata and reciter of Bhagavad Gita. However, in the original Dasavatara stotra, Balarama, the elder brother of Krishna, is stated as the eight incarnation, while Krishna (Lord Kesava) is the source of all the incarnation.
Kalki ("Eternity", or "time", or "The Destroyer of foulness"), who is expected to appear at the end of Kali Yuga. Story can be found in the Kalki Purana.
In the Bhagavata Purana.
As many as forty specific avatars of Vishnu are mentioned in the Bhagavata Purana, though the book adds that the number is innumerable. Twenty-two avatars of Vishnu are listed numerically in the first book:
Four Kumaras [BP 1.3.6] - the four Sons of god Brahma
Varaha [BP 1.3.7]
Narada [BP 1.3.8] the divine-sage who travels the worlds as a devotee of Vishnu
Nara-Narayana [BP 1.3.9] - the twin-sages
Kapila [BP 1.3.10] - a sage and one of the founders of the Samkhya school of philosophy
Dattatreya [BP 1.3.11] - the combined avatar of the Hindu trinity Brahma, Vishnu and Shiva.
Yajna [BP 1.3.12] - the lord of fire-sacrifice, who took was the Indra - the lord of heaven
Rishabha [BP 1.3.13] - the father of King Bharata and Bahubali
Prithu [BP 1.3.14] - the sovereign-king who milked the earth as a cow to get the world's grain and vegetation and also invented agriculture
Matsya [BP 1.3.15]
Kurma [BP 1.3.16]
Dhanvantari [BP 1.3.17] - the father of Ayurveda medicine
Mohini [BP 1.3.17] - the enchantress
Vamana [BP 1.3.19]
Parasurama [BP 1.3.20]
Vyasa [BP] 1.3.21] - the compiler of the scriptures - Vedas and writer of the scriptures Puranas and the epic Mahabharata
Rama [BP 1.3.22]
Balarama [BP 1.3.23]
Krishna [BP 1.3.23]
Buddha [BP 1.3.24]
Kalki [BP 1.3.25]
Besides these, another four avatars are described later on in the text as follows:
Prshnigarbha [BP 10.3.41] - the son of Prshni
Hayagriva [BP 2.7.11] - the horse-faced avatar
Hamsa [BP 11.13.19] - the swan
Golden avatra [BP 11.5.32] - the avatara in Kali-yuga for propagating hari-namasankirtan.