Full melt describes hash that melts readily with very little solid residue. Rosin is a concentrate separated from flower or hash using heat and pressure. Full-melt hash and hash rosin can share a starting-material history, but they are different finished products, and neither is automatically the better purchase.
One keeps the separated resin-gland material as hash. The other sends it through a press. That distinction tells you more than any claim that one is simply the stronger version of the other.
What each name establishes
Full melt is an informal quality claim about melt behavior. Hash rosin identifies hash as the input to a press. Full melt isn't a laboratory certification, and hash rosin isn't a melt grade.
Lowtemp's comparison lays out the process difference: bubble hash comes from ice water, agitation and screens, while rosin comes from heated plates and pressure, with bubble hash among the materials that can go into the press. Lowtemp sells pressing equipment, and its view that rosin is the more refined, cleaner-tasting product is its own. The part a buyer can use is simpler. Hash can be sold as it is or pressed further, and more processing doesn't settle personal preference.
How each one behaves in the jar
Lowtemp notes that bubble hash keeps a grainy consistency while it stays frozen, and at room temperature partly melts and turns tacky. Rosin can be finished into several textures; Lowtemp lists budder or badder, sap, shatter, jam and sauce. So the word “rosin” alone doesn't tell you how a jar will handle, any more than “hash” does.
Producers spell this out by product. 710 Labs' storage page lists its Persy Water Hash, Persy Rosin and Live Rosin under frozen storage. Its Persy Rosin Badder, Live Rosin Badder and Persy Sauce get a room-temperature window of up to three days, then the fridge for up to two weeks. Even within one producer's rosin, the finish changes the advice. The practical question is how this particular jar is meant to be stored and handled.
Individual jars vary inside a category too. The Wooksauce OGZ × Giraffe Puzzy review describes a freeze-dried bubble hash that was greasy and unstable rather than a pile that held its shape. The reviewer would buy it again. That account doesn't establish a six-star grade or show what pressing would have changed.
Compare within one source when you can
If a producer offers hash and rosin from the same cultivar, compare their descriptions and your own impressions with the format difference in mind. Two unrelated jars from different farms can't isolate the effect of pressing. A same-source pair is about as close as a shopper gets to seeing what the press changes, provided the source and batch identity stay visible.
Check package weight and final price before judging value. A star rating, a pale color or a higher THC number can't decide the purchase alone. The quality guide explains what those signals leave out.