I doubt that there is an unambiguous, consensually agreed upon definition of the difference between these terms, or that they're intended to have terribly distinct meanings here: I think it's more that the drafters are just trying to "hedge their bets" by putting various synonyms (I'm surprised they didn't add "fake").
However, if there is any difference, then perhaps it's this (based on Black's Law Dictionary):
- a "false" document is simply one that isn't genuine
- a "forged" document is a false document that is "fradulently made" or a real document "alter[ed] [...] to be used as if genuine" or one "made to look genuine by someone with the intent to deceive"
- a "counterfeit" document is a forgery that reproduces a trademark (or presumably other stamp/seal in this case) for the purpose of deception.
But, you shouldn't necessarily rely on these as being "the" definition. In an actual case, if there was any doubt then what would happen is that lawyers would lengthily and expensively fight it out between them as to whether they believed that a particular use was covered by these terms.