On reading about IMSI catchers, it is almost always mentioned together with MITM attacks, i.e. as if IMSI catchers are same as MITM.
But from my understanding, IMSI catchers and MITM are not the same thing:
IMSI catcher - as its name hints - only catches nearby IMSI number. For this purpose the fake BTS can connect to the mobile, without forwarding the inbound/outbound calls.
On the other hand, MITM allows the fake BTS to connect to real network, (just like a proxy) so that data from/to attacker is still flowing quite the same as before, except that it is now going through the fake BTS too.
So, is it correct to assume that IMSI catcher does not forward calls from faked BTS to the real network?