Answer:
The official name for football is of course football.
The football association is where the nicknames assoc or socca come from, as rugby union is often called rugger. These are nicknames and not the official names.
Yes
Answer
Soccer is another name for Association football. The word Soccer started as a phonetically abbreviated vernacular word for Association football coined by English public school students who took the 'soc' from 'Association' and put an 'er' on the end. The same students called Rugby football 'Rugger' but this word has largely fallen out of use. Typically 'an Oxford University student who played Association football and Rugby football' would be described as "an Oxforder who plays Soccer and Rugger". This is why prior to 1863 the word Soccer did not exist.