The third incarnation of Viṣṇu, Kṣīrodakaśāyī Viṣṇu, is the incarnation of the mode of goodness. He is also the Supersoul of all living entities, and He resides on the ocean of milk within the universe. Thus Caitanya Mahāprabhu described the puruṣa-avatāras.
Lord Caitanya next described the līlā-avatāras, or "pastime" avatāras, and of these the Lord pointed out that there is no limit. Still, He described some of them—for example, Matsya, Kūrma, Raghunātha, Nṛsiṁha, Vāmana and Varāha.
As far as the guṇa-avatāras, or qualitative incarnations of Viṣṇu, are concerned, they are three—Brahmā, Viṣṇu and Śiva. Brahmā is one of the living entities, but due to his devotional service he is very powerful. This primal living entity, master of the mode of material passion, is directly empowered by Garbhodakaśāyī Viṣṇu to create innumerable living organisms. In the Brahma-saṁhitā (5.49) Brahmā is likened to a valuable jewel influenced by the rays of the sun, and the Supreme Lord, Garbhodakaśāyī Viṣṇu, is likened to the sun. If in some kalpa there is no suitable living entity who can act in Brahmā’s capacity, Garbhodakaśāyī Viṣṇu Himself becomes Brahmā and acts accordingly.
Similarly, by expanding Himself as Lord Śiva, the Supreme Lord is engaged when there is a need to annihilate the universe. Lord Śiva, in association with māyā, has many forms, which are generally numbered at eleven. Lord Śiva is not one of the living entities; he is more or less Kṛṣṇa Himself. The example of milk and yogurt is often given in this regard: Yogurt is a preparation of milk, but still yogurt cannot be used as milk. Similarly, Lord Śiva is an expansion of Kṛṣṇa, but he cannot act like Kṛṣṇa, nor can we derive the spiritual restoration from Lord Śiva that we derive from Kṛṣṇa. The essential difference is that Lord Śiva has a connection with material nature but Viṣṇu, or Lord Kṛṣṇa, has nothing to do with material nature. In Śrīmad-Bhāgavatam (10.88.3) it is stated that Lord Śiva is a combination of three kinds of transformed consciousness known as vaikārika, taijasa and tāmasa.