Specimen/Unc Coin

It does depend in large part on which country's coinage you're talking about. As a general definition, "specimen" coins are struck on specially prepared planchets with specially prepared dies, with extra care taken to ensure coins are defect-free - rather like proof coins, except the quality isn't quite as high, the coins are only struck once by the dies (rather than multiple times fro proofs) and there's no "frosted finish" effect employed.

"Uncirculated" coins are simply standard mass-produced circulation coins that haven't actually been circulated, or are coins struck to the same standard.

Note that when the RAM uses "uncirculated" to describe many of their products such as mint sets, they really mean "specimen" by the above definition - since coins placed in the mint sets are specially and carefully made (often in the previous year) rather than plucked from out of the regular coinage production lines.