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a summer law clerk and a summer associate? I'm a law clerk, and I've been writing research memos, motions, responses, etc. - what would a summer associate typically do?

I am technically a 1L SA and I do all of those things.

From what I gather it's mostly a matter of semantics.
Big firms that have designated programs for summer law-student employment call these students summer associates.
Small firms that hire students for the summer don't seem to use that term.

I am a summer associate with a big firm, and I am called a SA and a summer clerk interchangeably. If you work for a judge after school, you are called a clerk, but other than that I don't think there is any substantive difference between the two terms.

I don't think there is a formal distinction.

Usually, firms that use the "summer associate" term are ones where the internship usually results in permanent employment.