As far as the Mark Twain where "fag" means much different in the US then than now - so do many uses of a word. Slang changes almost daily - think of words that are used now in slang ... "snatched" is a new one - used as a compliment - I think it means much different than just a few years ago.
And similar across the pond - and you mentioned that fag meant something different in one area than any where else. It is like that in the US as well - tonic in new england is different than anywhere else in the country, for example. It seems we call different dairy/ice cream beverages differently through out the country as well - a milk shake will have different ingredients depending on what part of the US you are ordering.
As far as word meanings throughout the years - read a classic from authors in your country - like Twain you will find lots of words or phases that would have a heck of a difference in meaning if you were to use them today in a conversation with your neighbor.
You are correct though it is quite interesting the difference a simple word can be whether it was a couple of hundred years ago - or miles apart.
I do still remember as a young adult - at a gathering at a friend's apartment with a couple of new friends that were recent transplants from Ireland - playing some sort of board game. The look on our faces when one of these Irish guys stood up and declared - I'm going to go outside and grab me a fag!