Arizona Kid and Handbasket are on target.
I recall Trail Lite and the Gulfstream BT Cruisers as being the first "B+" monikers. And 2002 is just about right too as I recall. I got hot for one of them when they first arrived on the scene and looked at a Trail Light down the road about three miles at the local dealer and then went 200 miles down to Colleyville, Texas ( Ft. Worth suburb) and bought a 2003 BT Cruiser. We had a Roadtrek 190 and I remember the first thing I had to do to the BT Cruiser was reinforce and reglue a lot of the cabinetry. It had two large closets and I converted one to shelving and hung a twenty gallon extra water tank under the chassis for boondocking. It was a good RV, but not a Roadtrek quality wise. Spent a little time fixing leaks and fixing stuff, but enjoyed the heck out of it until we traded four years later for a Roadtrek 210P.
B+ was and obviously still is a great marketing name because we are still discusing, cussing and arguing about its validity a dozen years later. It stuck in the popular vernacular. Back then (and I think still today) it simply represents a C without the bed over the cab. That was the original intent and filled the gap between a conventional C and a B.
I bet there are a hundred threads on this B forum over the years with purest quoting RVIA and they are absolutely correct technically. But the buyers call them a B+ and either is fine with me. Shoot, I like wine out of a box as well as in a bottle so I don't much cotton to worrying about purity of definition.
Paul