Not quite. In fact very different.
Vinyl in all it’s branded names is vinyl. A crude oil derivative. It’s usually bonded to a polyester backing.
PU “leathers” that people generally know as “fake leather” are polyurethane which is actually highly breathable, doesn’t trap heat and can be very scratch resistant. There are definitely different grades and combinations of polyurethane upholsteries and the modern auto developments are light years ahead of cheap furniture coverings.
For many years, BMW, for example, have used a split genuine leather hide liberally coated with polyurethane as their base “leather”. It is extremely durable but it trades that with comfort compared to their true leathers.
There really are some modern polyurethane upholsteries that are preferable in car interiors. BMW’s Sensatec is pretty incredible and some new buyers are preferring it.
I’m with you on wool based fabrics tho’, nothing like the comfort, durability and look of a felted wool on a seat.