Hi amma, whippets are yet a third breed. If you line up the three breeds next to each other, physically they're very similar. Greyhounds are the largest (generally 60 - 70 pounds), whippets are medium sized (perhaps 30ish pounds), and Italian greyhounds are the smallest at 8-12ish pounds.
Greyhounds and Italian greyhounds are both ancient breeds with examples in the artwork from ancient Rome as well as medieval Europe. Whippets are a recent breed, developed by mixing smaller dogs with greyhounds to achieve a slightly sturder, medium sized sighthound. All can participate in amateur racing and lure coursing sponsored by various dog associations. In the AKC, the Italian greyhound was shown in the toy group, but I think they recently changed that so they show with the hounds.