In both cases the speaker knows what word they're trying to say and both have difficulty getting the word out. But that's really where the similarities end. People who stutter eventually get the word out (usually). This is not necessarily the case for Broca's aphasia (of course, this depends on the severity of the aphasia, thus the severity of the stroke). Broca's aphasia (and all aphasias) are a result of brain damage, most often a stroke. In comparison a neurologist would look at your or my brain and say, "this is a normal brain."