Any bike can be a commuter. It is the act of going from work to home that makes it a commuter not how the bike is designed. However, certain bikes are more suited to particular commutes than other bikes. Not to mention personal preferences and riding styles.
Though I would be hesitant to call a bmx bike a commuter. That would be an amusing sight.
Commuters I have encounterd ride many of the following
-road racing bike
-road sport
-touring
-cx
-hybrids
-mountain bikes (hardtail, full suspension, and everything in between)
-recumbents
- and more I can not remember at the moment