On proofs the edges tend to be square and polished on plain edge coins, square and razor sharp bit not polihsed on reeded edge coins. I would expect PL and DMPL edges to just be like regular circulation strike edges because the PL and DMPL are related to the surface conditins of the die, not the striking pressure. Specimens, who knows what they heck those things are. I think "Specimen" is a term the
TPG's just pull out of a hat when they have some high quality issue that they can't figure out what to call it. Many of the coins called SP have also been called by other names at different times by the
TPG's until they finally settle down to the SP designation. For example the 1997
Jefferson nickel form the Botanical gardens set. It has been called at different times and by different companies Satin, Matte proof, Proof, SMS, and SP. So what the heck is it? It's "different" is all we can really say.
Or the 1927 SP
Buffalo nickels, They didn't make proofs that year, but these look like proofs. How were they made? We don't know. Why were they made? We don't know that either. Where they made specifically for someone? Again we have no answer. But they look different from normal, so they called them SP. Why? Because they didn't have anything else to call them.
Specimen can mean just about anything, so you ca't really say anything meaningful about their edges.