Difference between FMCF and AIMS on B777?
The B777 uses an Integrated Modular Avionics (IMA) architecture. AIMS is the modular computing platform on the B777. It's basically a bunch of computers in a box with it's own back plane network and operating system. It replaces multiple unique stand alone computing boxes. 

FMCF is the software that performs the Flight Management function. It is loaded onto the AIMS platform. In older aircraft architectures (B737, B757, B767) it was contained within a dedicated stand alone Flight Management Computer. In the B787, AIMS was replaced with the CCS (Common Computing System). It also has an FMCF software function.