I don't really know what the definition of it should be (or even what I really think it is), but in most cases I seem to think of "old school" as older looking cars (like, pre-80's) such as Mustangs and TA22 Celicas and old Corollas, I think generally cars with round lights :) that are "sporty". Sort of the "old school muscle car" look.
The word "Retro" seems to bring to mind things more like Cadillacs and Bel Air's and other sort of Old American Luxury Car sort of looks, although that's probably incorrect in definition?
And yes, I do believe than an old car should look like an old car, as in to keep in it's era, if it wants to stay in the "old school" camp. I don't think "old school" cars with new bits are wrong or ugly necessarily (although some really are), but they become a whole different car with all the bits added on.
For instance Rollie (or the car that was once Rollie anyway) was cool, even with the 17" rims and Evo-style bonnet scoop etc. It wasn't really "old school", and it wasn't really "modern", it was sort of a mix between the two...