Bb4 or Be7?

When I am learning Queen's Indian, there is a point which is a little hard for me to understand.

For example,

Black plays Bb4 in 4. ..Ba6 line.

But in 4. .. Bb7 line

black plays 5. ..Be7 more than 5. .. Bb4.

What's the difference between Be7 and Bb4? Why should black play Bb4 in 4. ..Ba6 line?

i'm not a qid expert but i know that in the ba6 line, specifically with the b3 subvariation that white chooses, black is trying to provoke bd2 and that's why he plays the tempo losing check. after bd2 the d-file is obstructed and the bd2 is going to have to move again anyway, and in the meantime c5 by black becomes a bit better if white' can't answer with d5 favorably.

in the old bb7 line i suppose you can still play bb4, but this time white did not have to play b3 and his bishop already stands on g2 which is a lot better for him.

I've transposed to this line a bunch of times (I play the English Defense).

It's not c5 you're preparing as black, but d5!  Be7 makes more sense in this context.  Ba6 only makes sense if the e-pawn has advanced, as it "pins" the c-pawn against Bxf1 when white loses the right to castle, but I think Bb7 is a fundamentally stronger play, as it's the fight in the center itself that really matters here.

Your target is d4, and the pawn must be effectively fixed on that square.  Realize that the move c4 has already softened the d4 square, so it makes the most sense to force open the d-file as quickly as you can.  However, you first need to get castled to do this, as otherwise checks/pins on the a4-e8 diagonal, as well as knights moving to b5, can be very troublesome.

There's a tactical idea that Black has, if White plays b3. Like this:

Now White's d4 pawn is under attack, and the only defending piece (White's f3 knight) is pinned. So White would have to push his position into disarray, in order to defend the weaknesses.

This is why Black plays ...Bb4+ in the ...Ba6, b3 line. Because if White blocks the check with Nbd2, then his position is suddenly difficult.

But if White correctly blocks with Bd2 instead, then Black simply returns the bishop to e7. White will have to move his Bd2 bishop again later, returning the tempo, so Black is fine.

So, short answer: ...Bb4+ is a prodding move, to see if White will make his position more awkward with Nbd2.

Beyond the concrete tactical point illustrated by TestPatzer, it also cuts down white's options. If black were to simply play Be7 white could also consider to develop with Bb2 or Nc3 should the opportunity arise. By starting with Bb4+ and only then Be7  those options are taken away from white, without anything being gained for it. So it's not simply hoping white might answer 6.Nbd2?!, it cuts down white's development options too.

This is a common idea in the whole Nf6 e6 complex for all the reasons mentioned already.  You see it in the Catalan for example to take d2 away from the knight.