A forgery is an item that was made to fool others into believing it is something it is not. This includes counterfeits, but also made up items like a ‘newly discovered’ Rembrandt painting.
On the other hand, a fake is an item that is seriously misidentified or who’s identity is seriously misrepresented. This includes forgeries and counterfeits, but it also includes items that are innocently misidentified by collectors or sellers who are uninformed.
When in doubt about a seller or maker’s intent, it’s best to call a bad sale or auction item a fake instead of a forgery or counterfeit. All three words mean an item is not genuine, but forgery and counterfeit implies intentional illegality.