The Nimzo-Indian is a very positional opening! After 1: d4 Nf6 2: c4 e6 3: Nc3 Bb4, we have the Nimzo
4: a3!? Bxc3 is the sämisch variation. White says: Give me the bishop pair and the centre, I'll win. Black says: You have weak doubled pawns, and the closed centre makes my knights stronger than your bishops!
From there, black often tries to close the centre, and place all his pawn on dark squares (to make his remaining bishop good), and play moves such as b6 Ba6 Nc6-a5 to attack the weak pawns. Sometimes white sacs the c4-pawn for attack, or black plays d5! at the right moment, winning the ¨c4 square¨ with a positional advantage. Very often white plays f3-e4-f4, with a great centre and strong attack. Black keeps his king in the centre as long as possible, since it's closed and white gets a strong attack.
After 4: f3, white says: I'll play e4, and you're dead! In the 4: .. 0-0 variation Black often plays Ne8(!) (to avoid Bg5 pin), and white plays a3, getting a superior Sämisch variation. But black will have alot of play on the weak pawns.
The rubinstein is the most positional variation, where white often avoid the doubled pawns, and hope to squeeze black with his superior space. In some variations Black plays: Be7!!, avoiding the loose of the bishop, and play d5-c5, saying that 4: e3 was too passive in a such positional struggle. White will play f3-e4 and hopefully use his centre to attack white.
In the Qc2 variation, White avoids locking the bishop in with e3, and will play the centre with e4. It has 1 problem. It takes alot of time after Qc2, a3 and Qxc3, so black will use his initiative to sac a few pawns and attack. He'll often take alot of positional weaknesses in return for more development, better piece play and attack. If white defends succesfully, he'll use his superior space and bishop pair to slowly squeeze black.
To answer you questions more directly:
The main idea in the Nimzo-Indian is either to double white pawns and attack them, winning the endgame (or losing the middlegame because of the white attack). If white avoids the doubling it takes TIME, which black will use to gain an intiative, often sacrificing or accepting positional weaknesses.
Against the rubinstein, black plays d5-c5, giving white an isolated pawn or hanging pawns (d4-c4 on open files), and both white and black should try to win on the pawn structure.
Against the Qc2 variation black will take the INITIATIVE for all costs, sacrifcing whatever needed! White will gain an edge if he allows to develop and use his bishop pair!
Is the main idea for Black in the Nimzo to restrain White from playing e4?
Can someone tell me the difference in Black's approach against the 4. Qc2 vs the Rubenstein lines?