The 1939 and 1940 Chevrolet and GMC grilles were very similar in overall design but they did differ slightly between each respective Model Year. The 1940 Model Chevrolets had a wider top grille than the 1939 Models but it is so difficult to tell from period photos.
1939:
Other changes included the switch to the new for 1940 standard of "sealed beam" headlights. This change forced the parking lights to be moved to the top of the front fenders like the cars, but the headlights remained attached to the radiator uprights as before. This was the last year for that characteristic. The top bar was located higher in 1940 had red 'Chevrolet' script. It appears as though the 1939 Models had script but it was not painted. That said that was for US-assembled civilian trucks and military versions often had painted instead of chromed grilles. The number of bars seems to vary according to the cab size...1/2 ton compared with 1 ton and above.
