While it looks like Wheels Up is adding some new offerings that mirror what JetSmarter does, that was not historically their business model.
Historically, Wheels Up functioned similarly to other jet card/membership programs (i.e. Marquis Jet Card, Delta Private Jets, Sentient, etc.). You join the program for a membership fee and then have guaranteed access to lift, subject to terms and conditions on peak day availability, minimum call out time, etc. for which you pay a set hourly rate depending on aircraft type.
Again, the traditional Wheels Up business model is chartering whole aircraft on your schedule. Just like Marquis, DPJ, Sentient, etc. (Sentient having gone through quite a few changes over the years and going back and forth between being an actual operator controlling a fleet and just acting as a middle man with no proprietary fleet)
Just as Marquis predominantly sources their lift from NetJets (Marquis is now owned by NetJets; they weren't always), Wheels Up is going to first source lift from its proprietary fleet of King Air 350s and Cessna Citation Excel/XLSs. Those King Airs and Excels are owned by Wheels Up but dry leased to Gama Charters who is the certificate holder that operates the flights.