Depends on intent. Did they make the coin to pass as a real coin in commerce, or to fool a collector? Then it is a counterfeit. Is it something like a 1964 silver dollar done by Daniel Carr? Then it is a fantasy piece. Many copies of ancients have been made for various reasons. Contemporary counterfeits made in antiquity are very collectible. Paduan copies were made in the Renaissance for collector, disclosing they were replicas. Museums used to make electrotypes for collectors of their famous pieces, not to fool but to share knowledge. Readers Digest and others made fakes in the 1960s as promotional pieces, not to fool anyone. Then you have modern fakes, only made to deceive collectors. All of these could be called copies or counterfeits, but in reality only the modern forgeries I would label counterfeits, the others not made to deceive, though they can deceive grandkids inheriting grandpa's "collection". Of course, contemporary counterfeits WERE made to deceive, but that was millenia ago and today they have a passionate collector base. TL/DR Make something today to fool the public or collectors and its a counterfeit. Do the same but not mean to deceive, its a "tribute" or fantasy piece.
If a counterfeit was made from a genuine silver or gold planchet, it could theoretically be worth bullion value.
Well, at least they followed the law. If they marked it COPY then its not a counterfeit, its a replica. No intent to deceive anyone. nothing wrong with replicas, they give some the ability to own something they otherwise could not afford. As to what you should do with it, label it a replica and do what you like. Keep it, give it to a kid, etc. If its marked per Hobby Protection Act, you are perfectly fine owning it.
Was it one of those traveling "clown shows" that advertise in the local paper and set up in town for the weekend?
No.. Your answer can be found at the TPG's website. Look for the type of coins they grade and what they don't. I know NGC has all that information.