Yes, FPGAs and ASICs (and CPLDs) are in a categories of their own, separate from microcontrollers, microprocessors and from each other. THe former are "designed" or "programmed" from a hardware persepctive while the latter are programmed from a software perspective.
An FPGA is reconfigurable hardware and so can be used to simulate the functions of different ASICs, microprocessors, microcontrollers, and CPLDs (depending on how you look at it)...at increased cost and sacrifice of certain performance characterstics however...