UI/Application Exerciser Monkey is a fuzz testing tool. The name is probably related to the fact that it behaves as if a monkey uses your application. It might be also related to the fact that (from Wikipedia):
"The Monkey" was a Macintosh application developed by Steve Capps
prior to 1983. It used journaling hooks to feed random events into Mac
programs, and was used to test for bugs in MacPaint.
The bottom line is that Monkey test and Fuzz testing are different names for essentially the same thing. However, there might be one subtle difference: while Fuzz testing is more about using random data, Monkey testing is about random actions.