Mufflers are generally part of the mower and not the engine.
Most of the mufflers are fairly close to the same size ( cheapness ) but the header pipes is where most variatios are so they fit in the space & the muffler is out of the way.
If the muffler bolts directly onto the mower they will interchange fairly easily by making up some mounting plates to suit the mower.
If the muffler is welded onto the header pipe it is a bit more difficult.
Thus most muffler fitted to mowers made by MTD will interchange regardless of what name is on the side of the mower and the same applies to AYP mowers.