At a cursory glance, these two terms appear to be synonyms. But that would strike me as unusual since one is a prefixed form of the other. (Prefixes are used to modify a word in a specific and consistent way. As a result, the prefixed form of a word has a different meaning than the word.)
"Per-" confers a quality of thoroughness or fullness. But in the context of ambulation, this doesn't seem like a significant modifier (to me).
Am I wrong, or are "ambulate" and "perambulate" synonyms?