CC Adi 1.65-66

īśvarera avatāra e-tina prakāra
aṁśa-avatāra, āra guṇa-avatāra
śaktyāveśa-avatāra—tṛtīya e-mata
aṁśa-avatāra—puruṣa-matsyādika yata

īśvarera—of the Supreme Lord; avatāra—incarnations; e-tina—these three; prakāra—kinds; aṁśa-avatāra—partial incarnations; āra—and; guṇa-avatāra—qualitative incarnations; śakti-āveśa-avatāra—empowered incarnations; tṛtīya—the third; e-mata—thus; aṁśa-avatāra—partial incarnations; puruṣa—the three puruṣa incarnations; matsya—the fish incarnation; ādika—and so on; yata—all.

There are three categories of incarnations of Godhead: partial incarnations, qualitative incarnations and empowered incarnations. The puruṣas and Matsya are examples of partial incarnations.