Specimen Silver Dollar Vs. MS Or Proof - How Can One Tell The Difference?

From what I know:

Specimens are struck slower, but with a larger pressure. The result is a nice, deeply struck coin with very square devices/lettering. The rim is also squared (full and deep) all around the coin. MS coins are struck faster with less pressure, and so your rims will not always be full. One side of the rim, you might see well struck denticles, and on the side of the rim you see flatter ones.

Specimens (as well as proofs) also have a brilliant finish for the fields, MS on the other hand has a cartwheel luster (it's not mirrored in the background). I think there a few exceptions, but in general that's how I go about it.

That's what I know for SP vs MS

As for Proofs vs SP, I can't help you much. For today's coins, you can distinguish between the two because SP has a lined/matte field with brilliant devices, while proofs are the other way around (mirrors field with frosty devices). But for older sets (I'm guessing pre 1990's here), both SP and PR have brilliant fields. Proofs tend to have frosty devices on both sides of the coins (or at least they do in my sets), but that's all I really know...

Hope this helps a bit! Someone should clarify between PR and SP because my answer is really vague