fag end vs tail end

fag end and tail end both are nouns.

Word	Noun	Adjective	Verb	Adverb
fag end	Yes	No	No	No
tail end	Yes	No	No	No

As nouns, fag end and tail end are synonyms defined as:

Other synonyms of fag end include tail.

fag end (noun)	tail end (noun)
the frayed end of a length of cloth or rope	the fleshy part of the human body that you sit on
the time of the last part of something	any projection that resembles the tail of an animal
	the time of the last part of something