What is the difference between homework assignment and agreement?

Semantics. Homework "agreement" is not generally a term accepted to have any significance.

The only condition to this would be if you and another individual had some kind of interpersonal agreement, and the executor chose to call it a homework "agreement," but this would have to be mutually agreed upon by all parties.

From a linguistic perspective, the difference between "assignment" and "agreement" is the direction of power in the interaction. Agreement is something done with mutual consent between parties; Assignment is something done by one party to another.

An example of an "agreement" situation would be between a therapist and a client, in which the client agrees to work on a project to help him/herself in later therapy sessions.

An assignment would be like a school assignment, where you are being instructed to do something by an authority figure.