The M122 has a block tread like you'd see on a car and traction qualities like you'd see on a drive tire (to move the rig forward), and it is described by Toyo as a "drive tire." The M177 is for steering and for trailers, Toyo doesn't list "drive" as an M177 application, and it has smooth highway ribs rather than a block traction pattern.
You'd need the M122 on the engine-powered drive axle, and probably elsewhere as well, although the M177 could fit the latter job too. The M177 would be right at home on a truck's trailer. The M122 might be a fitter fit, especially on the drive axle.