The simplest answer for a your original question is still "pull the cover and look if you want to know 100% for sure what you have".
If it's impractical to remove the cover for whatever reason, here are some quick checks to get a general idea what's in your axle without the need for disassemby:
-Equipment required: One floor jack (apppropriately rated for weight of vehicle), two jack stands, one wheel chock.
-Time to complete task : about 5-10 minutes.
-Skill level: Easy
The basic operational check for a Detroit locker is to pull the vehicle forward into your shop bay or driveway. Turn off engine. Jack up *one* side tire off the ground with transmission in park or if manual trans equipped, left in gear. Do not leave the trans or t case in neutral, driveshaft needs to be held immobile for this check. Remember to leave parking brake off if checking the rear axle. To make this a little easier to explain, just picture everything from the hand right side of your truck, with only the right rear tire off the ground. You should be able to spin the tire forward (clockwise) and you will hear/feel a faint clicking from the diff - don't worry that's normal. Try spinning the wheel backward (counterclockwise) and you'll feel the locker engage with a solid "clunk"and you won't be able to move it more than a couple degrees of rotation. Note that there's some "slop" or backlash designed into a Detroit for it to work properly, so you can turn the wheel a little bit backwards, just not very much. Detroits work by letting the outside wheel overrun the inside wheel during a turn so with this method you're basically simulating that driving condition. When both wheels are turning at approximate the same speed, the locker stays locked . Locked is the default position for a Detroit locker so it's only active when it's UNlocking - that's what you're checking to see if it does.
Supposedly if you back the vehicle up a hill and try the above or make a long pause in reverse before shifting to park, the free/locked directions above will be swapped around because of the way the outside cams are being loaded against the center spider (essentially, your truck "thinks" it's making a turn, but while traveling in reverse) I can't confirm the reverse thing because in the few times I've checked mine, I never actually tried it like that, but it makes logical sense if you have a pretty good grasp of
how a Detroit locker works. Important part is that the tire in the air is going to lock up turning one direction and spin freely in the other. A single wheel can spin faster than the ring gear, but never slower than the ring gear. With the truck in park the ring gear can't move so it's relative speed is zero and with the opposite tire on the ground, the other axle's relative speed is zero. If the tire off the ground locks up turning BOTH directions with the other side's wheel and driveshaft are both prevented from movement then it's NOT a Detroit locker, you've got something else. I mention this because a lot of people expect you can't spin the tire at all, truth is you can spin the tire by hand with very little effort (the locker unlocks) but you're only going to be able to turn it one direction. It is possible to break the teeth on just one side of a Detroit locker, so if you know for a fact your truck has a DL and you're just doing a function check because of some odd noise or driveability problem, repeat the whole process on the other side. Gov-locks are the opposite, default is unlocked and they only lock up when wheel speeds become significantly different, so none of the above applies. (This also is why Govloks have tendency to blow up if the driver is real throttle happy during slippery conditions)
So what if you don't seem to have a Detroit locker after doing the above quick test, what's next?
To tell a limited slip from an open diff, if the vehicle is in park with only one wheel off the ground, you aren't going to be able to spin the tire either direction without putting the truck in neutral so the driveshaft can rotate freely. To differrentiate an open diff from a limited slip the usual method is to jack the whole axle off the ground so both tires are off the ground and then spin one tire by hand while watching the other side. With an open diff the wheels will rotate opposite directions (one fwd, one reverse), with almost all limited slips the clutches will drag enough so that both wheels will be rotating the same direction. There are a couple oddball types of limited slips where this won't be true, but it's generally a pretty reliable indicator. If the vehicle has a spooled or welded rear you wont be able to spin the tire either direction if the opposite side tire is still on the ground regardless of whether the truck is in gear or neutral. A spool is 100% locked, 100% of the time.
If you do the limited slip vs open test first (both tires off ground), and both tires turn the same direction that still doesn't mean for sure that the vehicle in question is equipped with a limited slip. A really mangled open diff with damaged spider gears, a detroit locker, and a welded/spooled rear will all also spin both tires the same direction. You can narrow it down further by lowering one wheel to the ground - spool wont spin at all regardless of whether transmission is in park or neutral - Limited slip will only let tire spin when transmission is in netral and will usually be pretty hard to turn - Detroit locker will do it's thing but only one dierction as described above with trans in Park.
Hope that clears up all the confusion.
-Matt