My ex-wife is British.She used to tell me that they spoke English and we speak American.
The old expression that the problem between Americans and the English is that they speak two different languages is true in a lot of ways.
When I married her, she had three kids. Two sons, 12 and 14, and a daughter, 17. They were raised in the U.S. from babies. The daughter remembered a little bit about England before they moved here. So, for the most part, they were raised here.
I still laugh when I think about what the two boys would do when they heard their Mom use the word "fag" when talking about cigarettes. They found that most hilarious, and would roll with laughter when she'd say "fag".
I too thought "fag" meant "to smoke a cigarette" for a long time, until an American friend pointed out to me what it meant to them! 'Faggot' was a word unknown to me until then.