That's what "minced" means in Australian, does mince not mean coarsely ground in other places? And I'd call roast minced tallow and assorted meats a "rissolle", and I think Americans call it a "hamburger pattie".
Very roughly, in American English (mid-Atlantic), you have "chopped", "diced", and "minced" as decreasing sizes of something chopped with a knife; and "ground" or rarely "force(d)" for something that has been through a grinder. We commonly refer to "ground beef" (what you make the majority of a hamburger patty out of, possibly with additives depending); starting with a better or at least more specific grade of meat might get a more specific name like "ground chuck" or "ground round".
Once you get into industrial cooking, you may also have "chopped and formed" or "slurry" which tends to be the bits of an animal you wouldn't choose by choice but that are still technically meat, rendered fine enough you can't tell what they used to be. (The classic sarcastic description of it as "lips and assholes" has a considerable degree of truth to it even to this day.)
There is also "pulled", most commonly applied to slow-cooked pork but sometimes other meats, which has the meat fibers separated *after* cooking by a sort of pseudo-carding process, traditionally by a couple of forks pulled apart repeatedly. This has most of the increased surface area / easily mixed advantage of something that is diced, minced, or even ground... but retains more fibrous structure and has far less of an implication that it's been mixed in with inferior cuts and all smushed together.
British English (and possibly others, apparently Australian) usage of just "mince" as a noun is rare to unheard of by itself, and increasingly uncommon even in such archaic constructs as "mincemeat", which when found at all these days exclusively describes a sweet pie filling. (Which, traditionally, did have meat in it in addition to the fruit, but these days may not.)