From memory a coin (from a numismatic perspective) must have at least A) a face value and B) be issued by a governing authority. Since fantasy coins have neither, why are they called coins even among numismatists? Wouldn't fantasy token or medallion be a better term?
A "fantasy coin" does have a denomination/face value, and does have a designated "country of issue". It's just that, for a fantasy coin, the face value has never had any legal tender status in the designated country, because either the country does not exist (true fantasies), the country de facto exists but its independence and right to issue coinage is not recognized by other countries (unrecognized coins), or the country does exist but the legitimate government of that country never authorized the issue of that coin (unofficial coins).
In short, a fantasy coin is trying to fool you into believing that it is a real coin. If you hold a fantasy coin in your hand it looks "exactly like a real coin", and the only way to find out that it is not in fact a "real coin" is to try to look it up in a coin catalogue. Even then, the catalogues sometimes get it wrong, if they are unaware of the non-legality of certain coins.
I would restrict the term "fantasy medallion" to a coin-like object which does NOT have a designated country stated upon it. A good example would be the "fantasy dollars" of China, struck to the same size as a Chinese dollar and with a coin-like overall design but featuring design elements never used for actual Chinese coins, like the "eight immortals" or "four famous beautiful ladies" series.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis