Snapper P21507BE Repower help

I have a self propelled Snapper Mower with model number P21507BE. The engine information is Model: 124707, Type: 3114-01, and Code: 90031325. While the engine is shot, the rest of the mower has many good years left, I believe. I have been looking on multiple sites for a new engine for this mower. The real problem I am having is that I know from hand-me-down experience (my dad repowered basically the same mower a couple years ago, the only difference is his is not electric start and mine is) that I have to have an adjustable throttle or the self propelled feature doesn't work (or else you use the transmission and the blade doesn't spin with enough speed/force to cut your grass), and I am having trouble telling whether a motor has an adjustable or fixed throttle. Some sites don't even mention the throttle, they only mention the governor. So my question is, is a mechanical governor a nonadjustable throttle? Do the two even relate to each other, or are they completely separate specs?