I'd still count GEnie as being closer to a BBS than anything else, even if it was larger and covered a broader area. Or maybe that was just the way I used it.GEnie was an online service and competitor to the likes of Compuserve, Delphi, Prodigy, etc. BBSes were much smaller operations.
I wouldn't call Wang's board or The Lighthouse small by any means, and those were definitely BBSes.