I know that the game which is called "football" in Europe is called "soccer" in the U.S. But I wonder to what extent this differentiation is strict. What do people from England call their favorite game in conversations with Americans? Is there a misunderstanding in this case?
First is a point of order—it's also frequently called "soccer" in South Africa, Canada, Australia, and New Zealand, among other English-speaking places.
The Wikipedia article on the topic is "Association football", which is the full formal name of the sport—its governing body FIFA stands for "Fédération Internationale de Football Association", which in English is "International Federation of Association Football". If you want to be perfectly unambiguous, just call it "association football", and you can be sure that almost no one will know just what you mean.
In my experience as an American, when English people are discussing soccer they call it "football" and when it becomes apparent there may be some confusion they clarify by calling it "real football", which is delightfully arrogant.
However, once it's been clarified which sport is being discussed, we Americans are perfectly capable of understanding they mean "soccer" when they say "football".
The name soccer is derived from Association Football in the same way that rugger is derived from Rugby Football. In other words, it has its origin in the upper class slang of boys' boarding schools. For this reason, among others, many English people dislike that name.
I wrote a little taxonomy of football, which I'll attempt to reproduce here:
The insets are descendants, not varieties.
I'm neither British nor American, but I'm fairly sure most Britons know about the word "soccer", so there wouldn't be big misunderstandings while visiting America even when they prefer to call the sport "football" themselves.
I imagine they might utter some clarification ...
...and probably some clever or slightly condescending remark about the fact that a different word is used. Or maybe even a little rant, like this one by John Cleese. ;-)
My understanding of the etymology is that "football" was originally a general classification for the ball games played by "the foot". "The foot" is a mediaeval / early modern term for those who couldn't afford a horse; you still see it in military writing where an army will be described as "ten thousand foot and two thousand horse" or whatever.
There were hundreds of varieties of mediaeval football, frequently being one village against a neighbour, or one half of a village against the other. They are often referred to as "mob football". Most of them included holding the ball in hand.
The development of formal rules in the nineteenth century saw various splits - at first between those who allowed players to advance the ball in hand (rugby) and those who required a player who caught a ball to stand still and drop-kick it (association).
Over time, association football banned all use of the hand, other than by the goalkeeper within a defensive area, while rugby developed into more and more of a handling game. American and Canadian football are two independent developments from proto-rugby (ie from the uncodified handling games before the Rugby Football Union codified the sport).
Rugby split into rugby union and rugby league in 1889, and the dominant game in an area gets known as simply "rugby" and the other will be "league" or "union". League is dominant in the North of England (the counties of Lancashire, Yorkshire, Cumberland and Westmorland) and in New South Wales, Queensland and the ACT in Australia; Union in the rest of England, throughout Wales, Scotland and Ireland, in the rest of Australia and throughout New Zealand and South Africa.
In Ireland, Gaelic football was a codification of a distinctively Irish game, while in Australia, an interaction between uncodified proto-Gaelic football and the availability of large cricket grounds produced the distinctive Australian Rules football.
In most places, the dominant code of football became known as simply "football", while the other codes had to adopt qualified names (so you have "American Football", known as such in Europe).
"Soccer" and "rugger" were Oxford University (ie upper-class) student slang for Association Football and Rugby Football in the late nineteenth century, and soccer was popularised as an alternative name for the sport, especially in places where another code had monopolised the "football" word. It's widely used in Britain for "association football", either to make clear which code is being referred to (go to one of the rugby towns and you'll hear "soccer" a lot) or for reasons of euphony (e.g. the TV programme "Soccer AM"). But, of course, "football" alone usually refers to association football in Britain.
In a context where it's clear, "football" can be used to refer to any code. In rugby commentaries on TV in England, a team might well be described as "playing beautiful flowing football", without any implication of the association game.
I live in Melbourne, Australia and there's this sport called Footy which is believed to be "the real football"! Irony of it is that they mostly hand pass the ball (good guess, it's not round!) and sometimes kick it around the field as well!
So, whenever they talk football here, visitors usually don't have any idea what they are talking about.
DifferenceBetween.net says that
And one answer from the Answers.Com says
One answer from Yahoo Answers says: