Do background checks look only at convictions or also arrests.

Depends on who is doing the checking and why. Most checks only show convictions. But an in depth check could also show arrests or charges.

You could also have your credit report included in an in depth background check. Most financial institutions do this to ensure the person to be hired is not up to their eyeballs in debt so they won't take any samples home with them (say from a bank setting).

You didn't say who was doing the background check and for what kind of job.

Arrests don't normally matter, unless there is a plea deal for probation to have charges dripped.

I see your other question about the National Guard, your arrests should not matter, ** unless there are a lot of them showing a pattern or problem.

Just answer the questions honestly, if they ask where you ever arrested, tell them.