Fish width is the maximum body depth. The widest distance from the BASE of the dorsal fin to the lower outline of the belly. Basically it amounts to how wide a fish has to open its mouth to swallow a fish;; this distance is called "gape". Distance does not include to the top of the fin; prey fins are compressed when being swallowed so they do not count when taking the measurement.
Whereas Thickness is how wide the fish is across the back; widest point from right to left side.