The term Italian Game is sometimes used interchangeably with Giuoco Piano, although the latter also refers particularly to play after 3...Bc5.
[1] The Encyclopaedia of Chess Openings gives the Italian Game ten codes: C50–C54 for the Giuoco Piano, and C55–C59 for the Two Knights Defense.
Another option for White is the aggressive Evans Gambit (4.b4), a popular opening in the 19th century which is still occasionally played.
After the more common 4...d5 5.exd5, Black generally avoids 5...Nxd5 allowing 6.Nxf7, the Fegatello or Fried Liver Attack, or 6.d4, the Lolli Variation, both of which are difficult to defend under practical conditions.
Alternatively, White can play 4.d4, which may lead to the Scotch Gambit after the usual reply 4...exd4.