It's a shame that with so many variations of the Cinquecento (500), there isn't a 500 Race... Fiat doesn't even have a manufacturer's championship!
On the name designation, just like VW's Beetle, the 500 had little upgrades made during its history. Every time there was an upgrade, the letter changed. Hence, the original 500 was produced from 1957 to 1960; then came the 500D (wasn't this on in GT2?) from 1960 to 1965; the 500F & 500L (very little difference between them) from 1965 to 1972; and finally the 500R from 1972 to 1975. The most produced model was the F and L, since it was the model that went to the international markets as well. There was also a 500 Sport (500S) , with side vents and a red stripe.
These are of course, the "classic" 500 editions. As far as I know, Fiat never stopped production of the nameplate, and I've seen many new Cinquecentos on the street.