e3 vs e4 in 1.d4 openings In some openings, like Nimzo-Indian, the usual e-pawn move is e3, while in openings like the KID, White can play e4.
Is there some guidelines to know when you can play e2-e4?
In the Nimzo-Indian, Black's entire opening strategy is built around restricting the e4 push. 1... Nf6 stops it immediately. 2... e6 prepares 3... Bb4, which stops it again. Black's takeaway from the opening is that white is generally only able to achieve e4 by making some concession.

In the King's Indian, Black makes no attempt to stop the e4 push other than 1... Nf6 which is of course only a temporary delay. 2... g6 and 3... Bg7 are both aimed at d4.

So, you can tell when you can play e4 by looking at the idea of Black's moves.