There's no real common modern usage of "Albion" except in the name of football teams (West Bromwich Albion, Albion Rovers, Stirling Albion) - so it doesn't really mean one more than the other in English. Some people might say it comes from an old celtic word and therefore refers to Scotland, others might say it's from Latin and refers to England or the whole island of Britain. I've no idea which is "right" but the word just doesn't come up in everyday English.

Aside from the football teams mentioned, just about the only context you may hear Albion is occasionally old poetry and literature, or the famous 18th or 19th century French use of "Perfidious Albion".

It morphed into the modern Alba for Scotland, stemming from the same source, but I'm not sure quite of the overlap from Albion to Alba.