Here are 9 different categories that are used.
1 ) large-size US type notes
2 ) US national bank notes (issued by local banks chartered by the US)
3 ) US fractional currency (notes from the 1800s of less than 1 dollar)
4 ) pre-US colonial currency
5a ) US obsolete notes (from private banks of the 1880s)
5b ) Confederate States of America notes
6 ) small-size US type notes (the size we’re familiar with now)
7a ) recent and general world paper money
7b ) older and rare world paper money
8 ) error notes, including printing, paper and cutting errors
9 ) Souvenir Cards
It’s a minting variety, caused by wear and tear, with one of the clad layers splitting off, either before or after the coin was struck. It could also have been removed after leaving the mint so it needs to be checked by a specialist. If it is a genuine error, it may hold numismatic value.
If the edge is reeded it is a slug, as there are known counterfeits of dimes and quarters made to use in slot machines that don’t have a design, but do have a reeded edge. If the edge is smooth then you have an unstruck planchet. A planchet differs from a blank in that the rim is raised on the planchet.
There are circulating coins, commemorative coins and circulating commemoratives so we need to look closely at our definitions. A circulating coin is one issued and intended for commerce, sometimes called a business strike. A commemorative coin is one issued, usually under a special law, to commemorate some historical event, person, place, group or anniversary. They are similar to medals, but they carry a denomination, a specific reserved to government issued coins. Circulating commemoratives combine the two divisions, in a coin which is both intended to circulate and to honor or commemorate something. The new State quarters are an example of a circulating commemorative, as were the Bicentennial quarters, halves and dollars issued in 1976.
It’s very probably a normal cent that either lost its copper plating, or missed the plating operation during manufacture. Since mid-1982 our cents have been struck on copper-plated zinc planchets. A specialist would need to examine the coin to determine if it’s genuine or an altered coin.
The original meaning of a proof was a coin struck to ‘prove’ the dies. More recently it has come to mean a coin struck two or more times with polished dies on a planchet which also has been polished. Thus a coin struck only once does not qualify as a proof. The US Mint sells proof coins in sets that come in hard plastic cases. You may still find a proof coin in circulation, discarded by a collector or dealer because of some defect. US proof coins are legal tender, just like regular coins.