I don't think that is correct re football. Football is an English invention.
It then split into Association Football and Rugby football.
From Association Football we get soccer. So Football was first then soccer.
e.g. The Football Association was formed in 1863 and the first international match in 1872 was billed as International Foot-ball Match and then in small writing (Association Rules) before the term soccer was used.
Ah you're right, I may have gotten my memory slightly mixed up. Even so, the name soccer (at least as a nickname) was formed in the UK, along with association football, both referencing the same thing, and which became more popular over time diverged across country lines, so the analogy isn't too poorly fitting at least!
From Association Football we get soccer. So Football was first then soccer.
e.g. The Football Association was formed in 1863 and the first international match in 1872 was billed as International Foot-ball Match and then in small writing (Association Rules) before the term soccer was used.