The “Fish” in all three of these postures is referring to the first avatar of Lord Vishnu. This myth first appears in the Shatapatha Brahmana (700-300 BCE). This story is one that we might be more familiar with than we realize…

Matsya keeps growing and growing, and Satyavrata continues moving him from one jar into another, always needing larger and larger containers, until he has no choice but to move him into the ocean…

This is possibly where we get the progressions of these postures. Each referring to a different period of Vishnu's transformation from a simple little fish, to the size of a 'half-king-fish' and finally into the form of a 'full-King' fish!

Matsyendra warns Satyavrata about the coming dissolution of the world…