You could take it apart in 10 minutes and know for sure. I've never had a Ford clutch type limited slip apart so I don't know what they look like. Its not a Detroit locker because they don't use pinions, and you can see a pinion cross shaft thru the side view.
Probably doesn't make any difference though, since there's a high likelihood the whole thing is junk. I've never seen a 9 inch third member with that much visible damage that didn't also have a crack in the casting where the pinion nose bearing rides. That you could grind up that much metal without anything getting inside the differential housing itself would be real unlikely. Bearings would obviously be shot too, and that pretty much covers every major part of the entire assembly.
Best I can tell, it looks like its come from something with 31 spline axles. If you're looking for something to go in a 79 F-150 4x4 like your screen name might suggest, you might have a real problem finding something used that will work. I had the same truck for about 20 years. One of the side gears split and chewed up the spline on one axle. That was in the first half of the 90's and even then it was near impossible to find anything used. 4x2 trucks used 28 spline axles. You couldn't just swap the 3rd member and axles from a 4x2 into the housing because there's a difference in the overall width of the housing itself. Ford wanted about $450 back then for one new side gear and one new axle. I'd be afraid to ask the price today, if the stuff is even available.
I had a complete 4x2 rear end with the same 3.50 ratio, so I relocated its spring pads and put it in the truck. In looking for parts, I'd talked to the owner of a big junkyard that specializes in pickups, and he said he usually had a waiting list of 10 or more people looking for the 4x4 rear end, and that he'd only get 3 or 4 trucks on average in a year with the right rear end. That was over 15 yrs ago, and I'd guess they aren't any easier to come by today.