Achizah, Tefisah, and Muchzak are basically the same thing. Achizah literally means "holding" and Tefisah literally means "grabbing." Muchzak literally means "holding," but also implies that the person has the status of being the owner of the object he is holding. In another sense, one could say that Achizah and Tefisah generally lead to someone being considered a Muchzak (meaning we should assume he is the owner unless proven otherwise, or unless he makes no legal claim that he is the owner).

All the best,

Yaakov Montrose