The term soccer comes from Oxford "-er" slang, which was prevalent at the University of Oxford in England from about 1875, and is thought to have been borrowed from the slang of Rugby School. Initially spelled assoccer, it was later reduced to the modern spelling.
“Football” almost always means soccer (association football) in the UK, but there are also things like rugby football and Gaelic football.
Edit to add: you need to disambiguate when other forms of football are popular (eg at Oxford university) but these days soccer is the most popular sport by a huge margin.