With due respect to the late Holy Father, it's worth pointing out that any vehicle he used in public seemed to get termed "the Popemobile".
Having watched a lot of coverage, and it's going to be repeated in the short term, he has certainly used vehicles based on Land Rovers, FIAT, Range Rovers, and Mercedes G-Wagens. For his UK visit in 1982 several were built, I think they are in museums, one was based on a Range Rover and another (much larger one) was based on a Leyland truck. I think that each country built something suitable for the visit, therefore the diversity was great, though the basic form was similar. These seemed to be better protected after the attempt on the pontiff's life.
Incidentally, regarding models, Ferrari presented the Pope with a 1/5th replica of their 2005 F1 car earlier this year.
Hope this is of help.
MH