The Ruy Lopez is a more aggressive opening than the Italian Game. This opening is more agressive because 3. Bb5 applies pressure to Nc6, which in turn applies pressure to the e5 pawn (because Nc6 is defending e5).
After this position, black’s best move is to play 4. a6 to apply pressure to white’s bishop. This is known as the Morphy Defense.
After the opener, white can either play 4. Ba4 or 4. Bc4.
• 4. Ba4 keeps applying pressure to Nc6 as it originally intended to. This is known as the Columbus Variation.
• 4. Bc4 redirects that pressure back into the Italian Game.
4. Bxc6, known as the Exchange Variation, is probably a bad idea. It welcomes black to play 4. dxc6. This will either invite black to play 5. Bg4, or if white plays 5. Nxe5, black then plays 5. Qd4. White is guaranteed to lose some material here if black chooses to do so.