Actually, if you look at requirements for a student pilot, they must be
signed off for each type of aircraft they will fly solo. Kind of a Type
Rating if you think about it. And while a student, I think a CFI can't
sign you off until you can prove you can do slow flight, stall recovery
and controlled landings in that particular type of plane.

When I first soloed, I did it in a C152. Because we had done training
in the C150 at that point, all I had to do for my instructor was make
two landings w/o him having to say or do anything - he then signed me
off for the C150.

After my PP, I was checked out in a C172 w/in 2 hours total time. All I
had to do was prove that I could land the plane, and do slow flight.
All the insurance company wanted was a CFI to say I could handle the
plane.

Later,
Steve.T
PP ASEL/Instrument