I believe that folks in England use the term soccer to describe the honchos upstairs aka the FA, or UEFA, or FIFA, or the Law Board, etc.
Association Football, or soccer (code)
American Football (code)
Canadian Football (code)
Rugby (League, or Union) (code)
Gaelic Football (code)
Aussie Football (code)
It isn't so hard to distiguish any of the football codes whatsoever, maybe the basic rugby forms might by confusing though.
So how do Americans know they are watching Canadian football? Easy, count 12 guys, find red penalty flags, wider and longer fields, deeper end zones, and the posts are at the goal line. Oh, and they punt on third down, not fourth.
It doesn't bother me to type Am. football when I mention football. Maybe soccer gurus can just type assoc. football, my thoughts.