After 1. e4 c6 2. d4 d5, what are the differences between 3. Nc3 and 3. Nd2?
It seems 3. Nc3 is more popular, though after 3. ... dxe4, I failed to see the difference.
3.Nc3 allows White to play the Two Knights Attack with
2.Nf3. It does block the c-pawn, though, so Black can play
3...g6, the Gurgenidze System, because White cannot protect the d-pawn with the c-pawn.
There is also the rarely played Gurgenidze Counter Attack
3...b5. A very dubious line that can be stopped easily with
3.Nd2 tries to avoid these lines, but it makes the Two Knights Attack impossible, a line that is very popular nowadays. It also blocks the view of White's dark-squared bishop, so Black can develop their kingside knight to
h6 if they want.
Nd2 avoids this line:
1.e4 c6 2.d4 d5 3.Nc3 b5!? 4.ed5 b4 followed by recapturing on d5
IM Jeremey Silman was a proponent of this for Black as a surprise weapon.
Yes, if Black plays 3...dxe4 there is no difference whatsoever.
The difference between 3.Nc3 and 3.Nd2 is the sidelines they allow/prevent Black from playing. For example, 3.Nc3 may encourage 3...b5!?, trying to harass the knight.