Being from the UK, I hear it all the time to refer to cigarettes. When I worked in a shop, my colleagues would just walk through the shop and say "just taking a f* break". While it was totally inoffensive, it did make me a bit uncomfortable. Piquing my sjw sensitivities, I guess
Personally I find it disturbing that adults discussing the word feel the need to type things like “f-word” instead of just typing the word fag. You’re talking about a cigarette. It’s a configuration of 3 particular letters. There’s no reason to react to them in that context.
There isn't any relation other than the word being used. It's not something I ever complained about because I understood that it wasn't offensive in any way and is, like I said, just the response I have to hearing that word.