‘Fag’ has two meanings in English, both colloquial, both very different; one is an offensive term for gay people, the other is a slang term for a cigarette. How has ‘fag’ come to refer to both?
The use of ‘fag’ to mean a gay person is a shortening of ‘faggot’ – which was a term applied to undesirable women in the late 16th century, it was coined as an Americanism in the early 19th century. Similar to words such as ‘nancy’ and ‘sissy’, it was intended to imply that gay men were effeminate, it was later applied to gay males and females. Its use to describe undesirable women in the 16th century was a way of implying a woman was so poor that they had to work collecting sticks to sell as firewood (a job considered very low), ‘faggots’ was a term for a bundle of sticks – from Latin ‘fascis’ which also meant the same thing.
Fag to mean ‘cigarette’ is from the 14th century English word ‘fag’ which meant ‘last remnant of cloth’, it was later (1610s) used to apply to the extreme end of anything and in 1888 was applied to the butt of a cigarette, from then it became a term for the whole cigarette.