The Model III and early non-gate array model 4 (separate floppy board) and the non-gate array 4P all use the FD1793. The gate array (single board) model 4 and the gate array 4P both use the WD1773.
The WD1773 is almost 100% FD1793 command-compatible in both FM and MFM modes, but is a physically smaller chip, 28 pins, and requires less circuitry external to the FDC to operate. While software can through some tricks determine which chip is in use, in practice they are fully software and format compatible.
Some third-party FDC boards used other, but still software-compatible, chips such as the Fujitsu MB8877 and MB8877A.