In different millennia there are different incarnations, and they are innumerable, although some of them are very prominent, such as Matsya, Kūrma, Varāha, Rāma, Nṛsiṁha, Vāmana and many others. These incarnations are called līlā incarnations. Then there are qualitative incarnations such as Brahmā, Viṣṇu, and Śiva (or Rudra) who take charge of the different modes of material nature.
Lord Viṣṇu is nondifferent from the Personality of Godhead. Lord Śiva is in the marginal position between the Personality of Godhead and the living entities, or jīvas. Brahmā is always a jīva-tattva. The highest pious living being, or the greatest devotee of the Lord, is empowered with the potency of the Lord for creation, and he is called Brahmā. His power is like the power of the sun reflected in valuable stones and jewels. When there is no such living being to take charge of the post of Brahmā, the Lord Himself becomes a Brahmā and takes charge of the post.
Lord Śiva is not an ordinary living being. He is the plenary portion of the Lord, but because Lord Śiva is in direct touch with material nature, he is not exactly in the same transcendental position as Lord Viṣṇu. The difference is like that between milk and curd. Curd is nothing but milk, and yet it cannot be used in place of milk.