In this answer, I will use some technical terms specific to our philosophy. If anything is unclear, simply ask for further clarification.
Krishna, Vishnu, and Shiva are all individual personalities.
Srimad-Bhagavatam clearly states that Lord Krishna is the origin of everything and everyone (krishnas tu bhagavan svayam), but the personalities are not like impersonal replicas of the Supreme Personality of Godhead.
Everything comes from the Lord’s numerous transcendental energies.
Shiva is an avatara, specifically a Gunavatara, and he takes care of the material mode of ignorance and destroys the universe when the moment arises.
The analogy of milk and yogurt is clear: Shiva is a divine personality, not a jiva like us, but he transforms when he comes into contact with material nature. Just as milk turns into yogurt when it comes into contact with an acidic substance, Shiva becomes a personality of a different nature when it comes into contact with Maya. Milk can become yogurt, but yogurt cannot become milk. It is a tattva in its own right. Srila Prabhupada calls it a Shiva Tattva.
The case of Vishnu is different, as he is both gunavatara and purushavatara.
There are three Purushavataras, and they too are individual personalities. The three Purushavataras are:
Maha-Vishnu (Karanodakasayi), Garbhodakasayi Vishnu, and Ksirodakasayi Vishnu.
Each has a specific role in material creation. The various incarnations, including Shiva, come from Ksirodakasayi Vishnu.
Maha Vishnu is the cause of Pradhana, the basis of material creation, which then transforms into Prakriti and finally into Mahattattva, ready for the specific creation performed by Brahma.
Unlike Shiva, Vishnu never touches material nature and therefore “remains milk,” always transcendental.
Manonatha Dasa (ACBSP)
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