Apropos Dick Johnson's comments on "wire edges," I would add that on coins (I cannot speak on medals) a more likely cause of wire edges is the slight misalignment of the hammer die, so that the outer edge of the die is not in perfect alignment with the inner edge of the collar. This creates a thin, crescent-shaped gap that metal can escape through, especially under multiple strikes such as a Proof would receive or a 1907 High Relief $20.
Over the years I have seen Morgan dollar Proofs that appear to have been very carefully trimmed around the rim, presumably to remove a wire rim. The precision and consistency of this trimming makes me believe that it was done at the Mint, though I cannot prove that.
The term “wire edge” is a generally misunderstood term bastardized by Wally Breen and friends. It is implied as some sort of identifier of proof coins or coins with better than normal details. Synonym for “hokum.”
Coins do not have “wire edges.” The term is often misapplied to a “fin” (or more descriptively a “fin rim”). A fin rim is a very thin extrusion of metal ("flashing" is good, too) sitting above and at the other edge of the rim. It is a minting defect caused by a mismatch between planchet upset, planchet size and the edge collar-die diameter. It can occur at normal striking pressures as well as high ones.
The best known examples are Saint-Gaudens MCMVII $20 made through mid-December 1907. The defect was largely corrected through changes made to the upsetting of planchets from mid-December until the last pieces were struck.
An often confused, but unrelated term is “knife rim.” A knife rim occurs when the field of the die face curves directly to the edge of the coin. The result is a sharp knife-like rim rather than a normal flat rim. This is an intentional part of the design.
Lastly, one more misused term: “rolled edge” or “rolled rim.” As abused when referring to 1907 $10 from the 2nd hub, this is supposed to be some sort of special rim applied to the coins. Nonsense. It is nothing more than a normal not-quite-flat rim as found on coins made on production presses, as were the 2nd hub 1907 $10.