remnant vs fag end

remnant and fag end both are nouns.

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

As nouns, fag end is a hyponym of remnant; that is, fag end is a word with a more specific, narrower meaning than remnant:

remnant: a piece of cloth that is left over after the rest has been used or sold
fag end: the frayed end of a length of cloth or rope

remnant (noun)	fag end (noun)
a piece of cloth that is left over after the rest has been used or sold	the frayed end of a length of cloth or rope
a small part or portion that remains after the main part no longer exists	the time of the last part of something