It really does vary state to state.
DH and I both had to retake the written test in Ohio this past summer, after our move from Texas. We were both still in the Ohio DL system, as we were issued our first driver's licenses in the early 90's in the State. But since it had been 15+ years from the last issue, we had to start from scratch. Annoying, but still I see their point.
When we got our licenses in Texas, we simply showed up and turned in our old Ohio ones in exchange for a temporary (paper) license for TX. All we needed was proof of insurance and a valid TX address. No tests, apart from vision, at all. Then again, I think TX has a *very* liberal drivers ed requirement for young/new drivers..