In the PCA (see BCO 22), the distinction is as follows:
1) Associate pastors are called by the church as the congregation at large, are brought on staff as regular session members, and assist the primary Teaching Elder.
2) Assistant pastors are called by the church as the session, they are not members of session and so do not rule the congregation, and they also assist the primary pastor and session.
Both Associates and Assistants are to be ordained men, and are members of Presbytery. Sometimes churches call men who are appointed to staff positions like "youth pastor" or other, and are called "assistant pastors;" but by the BCO, those are NOT true pastoral relations, because they are not called by the church, examined and approved by Presbytery.
Temporary relations of pastors to sessions are known as "Stated Supply," usually created in transition periods between solo/sr. pastors at a given church. These men serve similarly to an Assistant, not being on the session, but at the request of the session. They typically moderate session meetings, but do not vote (rule) over the congregation.
Real world example: myself. I'm an Assistant pastor at my church. As of January (sr. pastor retired) I am now Stated Supply at my church. My relation to this session or congregation has not fundamentally changed, except that I am temporarily the regular preacher and tasked with all the regular pastoral duties of a sr. pastor. And I also moderate the session meetings, but not as a member (as is also the case with most Stated Supply ministers brought in from outside the church).
When (or possibly before) the new sr. pastor is called, I will step out of the Stated Supply role. In fact, I should be moving on (someplace) to another call, D.V.