Wow, thanks @Vanaroo I had no idea. Yep, I'm Class C for sure.There are quite a few Class C's without a bed over the cab. And some that do have one but still don't fit the stereotype of the big boxy typical one (eg Tiger on pickup chassis).
Here are some you could Google if you'd like to see (not trying to be stingy by not posting a photo of each one but I don't want to make people reading a thread about Class B camper vans scroll through a dozen photos).
Tiger (on the Astro chassis with no cabover bed or on a pickup truck chassis with a bed over the cab)
Starflyte by Dynamax
Gulfstream BT cruiser (older ones were around 21-22')
Leisure Travel Unity
Leisure Travel Libero
Chinook Concourse and Premier (they also made an even more vintage class C on the Toyota pickup chassis)
Pleasure Way Phoenix
Basically if you search "B+" you will find most of the Class C RV's that marketers want to "set apart" from the Class C category. Usually because they are relatively much more expensive and Class C's had a reputation for being big cheap boxes with cabover beds. Basically the same reason you were thinking (so I guess their marketing ploy has worked ). Still Class C's though (I say, be proud of your cutaways; no need to make a new category).
It's ironic though as many of the "B+" are now 26 or more feet long with slides, surpassing the size of many typical older Class C's (and some have insane overhangs in the rear - I don't know how people get those into a gas station with an angled driveway without ripping the back end off).