fATPL = CPL + ME/IR + MCC with the full set of ATPL (rather than separate CPL and IR) written exam passes. Legally speaking however, it's still just a CPL/ME/IR.
ATPL = fATPL with at least 1500TT of which 500 multi-crew then an ATPL kill test, required to command a multi-crew aircraft with pax on board.
Modular = doing the bits you want / need, in your own time, under your own management, with one or more training providers. Requires at-least 250 hrs.
Integrated = doing the fATPL from zero to hero with a single training provider, approved to do this by the CAA, no separate hourbuilding, no separate PPL, can I think be done in 175 hrs. Preferred apparently by some airlines, disparaged by many in other flying environments as overpriced and creating pilots who are incapable of doing anything but operate to strict procedures in a corporate environment.
Typical bill for modular fATPL ~£50k
Typical bill for integrated fATPL ~£90k.
There are two reasons for a European not to go to a US aviation department:
(1) An FAA licence isn't useable in Europe
(2) The degrees they award are pretty much worthless academically.
G