Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6/3. Bb5/3...f5/4. d3/4...fxe4/5. dxe4/5...Nf6/6. O-O/6...d6

Now that Black is no longer vulnerable to Nxe5 tricks, the e4-pawn needs to be defended. The economical-looking 7.Re1, normally a very sensible move in the Ruy Lopez, would be dangerous in the Schliemann because it would weaken f2, the target of Black's future pressure along the f-file.
 * 7. Nc3 develops an undeveloped piece to its natural square. Nothing wrong with that!
 * 7. Qd3 is a move that's recommended against 6...Bc5, because after 6...Bc5 7.Qd3 O-O?? White simply wins a piece with 8.Qc4+, so Black is prevented from castling for a while. However, there's currently no bishop on c5 to win, and if White wants to prevent Black from castling after 7.Nc3 she always has Bc4. White may also lose a tempo if Black's light-squared bishop comes to g4 and swaps itself for the f3-knight, because the queen could have recaptured directly from d1. On the positive side, putting the queen rather than the bishop on c4 has the advantage of maintaining the pin on the c6-knight that Black brought upon herself by playing 6...d6. Results-wise there isn't much to choose between the two moves.