Regarding the engine mounted to the frame in the first few pics. It looks like a craftsman engine from an edger. based on the dipstick and air cleaner The recoil may not be original to the engine as the original recoil would have been riveted on and now has screws. The recoil appears to be a lawson/ early tecumseh stamping which predates the engine .The carb is newer than the engine because it has a fitting for a breather hose on top. The original would have been a diapragm carb. Your close up pics are kinda too close to tell but if it has a side exhaust and the four bosses in the side cover are not tapped ,its definetly an edger motor. Another clue is the spacer on the rear head bolt for the rear mount one quart tank.
Regarding the other engine it is NOT original to the fat tire roper as the roper came with a 4hp small frame engine ie., Hs40 rebadged as a Craftsman 143,xxxxxx with a 2qt front mounted tank. That 6 horse wont even fit in the frame with tank and air cleaner set up.
Post more pics of the first engine and I can give you a better answer.