All I own are road bikes. Two of them also have rear racks and fenders, but I commute on all four of them, depending on weather and if I need to haul anything that day.
According to my Websters Unabridged, commute is a verb, or something you do. Commuter is a noun, or a person or thing. Therefore, you can commute on anything, even your daughter's Barbie bike. Only in marketingland do you require a special "commuter bike". Fortunately, I live in reality, not marketingland.
I prefer road bikes.