American football can be referred to as gridiron football. Soccer can be referred to as futbol
and many people in the States would know you mean soccer.
we all know it is the sort of football where the foot is barely used, if ever.
That'd be incorrect. In gridiron football, the foot is used often and at essential times. Kicking field goals, kicking the point after (a touchdown), at the kickoff at the beginning of possession, and a few others incidences (squib kick or offside kick).