The difference between an authentic and replica soccer jersey is that the team or players in question endorse authentic jerseys while replicas are sold by licensed distributors, but not endorsed by the team or players. The terms are easily confused, and some replica shops will also use "authentic" in their marketing.
There are also kitroom jerseys offered for sale toward the end of a soccer season. Kitroom jerseys were originally made for the players, but for various reasons, didn't get used. These are often referred to as authentic, or sometimes "player shirts," but the more accurate adjective is kitroom, or sometimes ex-kitroom. A grade down from replica shirts are the fan or stadium shirts, which use cheaper material and transfer logos instead of embroidery. Next are the fake shirts, which are knock offs and use the cheapest material. Fake jerseys do not last long.