In British English, Jersey doesn't mean uniform. We don't even really use it at all (except to refer to the island). Where as uniform would be almost universally used, in the context of military uniform, sports team uniform or school uniform. Don't fall into the trap of learning "American"
Sorry, Jlsalisbury, but that's not true. I have never heard "uniform" used on the eastern side of the Atlantic for what a sports team wears (at least not in the most popular sports - perhaps there are some minority-interest sports where it is used). The usual terms, as of now, are "strip" or "kit". Apparently, in the US, it's called a "uniform". When one hears "uniform" on this side of the Atlantic, one thinks of the military, the police, boy scouts, school uniforms, etc., but not teams that play a sport. A search for the term "football jersey" (which is used to refer to the top part of what footballers wear, not the rest) on Google (Feb. 2021) turned up over 8 million links, most of them non-US as far as I can see.
A ,uniform"" is worn by a member of an organization, primarily an army/armed forces/a nurse/a police officer. A sports team plays in its "playing kit" or ,"sports kit". No one would refer to a footballer's/sportsman's uniform , except maybe in North Korea or some other authoritarian country. Do RU footballers really refer to their "uniform"?