And rugby is actually "Rugby Football," as I learned from the local Medway Rugby Football Club.

There's association football (soccer), rugby football, gridiron football (American and Canadian), Aussie rules football, and probably others either in certain niches or in the past. I've been calling the NFL and CFL "gridiron" exclusively for a few years to avoid any confusion.

In Australia, Rugby League and Rugby Union can both be referred to as just “football”, though there are also other more distinctive terms for the sake of clarity: https://en.wikipedia.org/wiki/Football_in_Australia#Terminol...

And they’re just two of the four major codes, two of the six if you include Gaelic football & gridiron which are both relatively minor.