'Italian game' refers to any game that follows after the sequence 1.e4 e5 2.Nf3 Nc6 3.Bc4. This includes both the Two Knights Defense (3. ...Nf6) and the Giuoco Piano (3. ...Bc4). 'Italian Game' is more accurate than Giuoco Piano, since this literally means 'Quiet Play' and most lines in the Evans Gambit and Two Knights Defense are anything but quiet, though I suspect the term 'Italian Game' started, because a lot of people just can't spell or pronounce 'Giuoco'.