Ask any FBA seller, especially those who do product arbitrage, and they'll tell you that Amazon is getting very aggressive with account suspensions and requiring a lot of documentation that the seller's original supplier is either the brand owner themselves or an authorized distributor.
I know a guy who did arbitrage with imports (authentic products, but "not authorized" because they were factory overruns). He made some good money for 2-3 months, but almost all of his products got removed for lack of verifiable paper trail and he ended up in a pretty bad spot.
These are counterfeit products. When you contract with a factory to make 10K units with your brand on them, they aren't allowed to use your brand to sell any number of "overruns" past that.
To most people, "counterfeit" does not mean literally the same product, produced by literally the same people, even if the company who commissioned the build didn't want some of those units to be released onto the market.
Personally, I dislike the suggestion that an identical product is "counterfeit" merely because the company that commissioned the product is seeking to constrain supply and keep their price point artificially high.
The contracts between the manufacturer and the client are unknown to buyers. If the contract is being breached, the client would probably be wise to seek to enforce the agreement.
I understand there are potential trademark implications (but afaik they're not necessarily cut and dry, IANAL), but IMO this doesn't classify something as a counterfeit product, at least as far as general usage is concerned. I make no comment on the legal classification/terminology.