by-election vs election

by-election and election both are nouns.

Word	Noun	Adjective	Verb	Adverb
by-election	Yes	No	No	No
election	Yes	No	No	No

As nouns, election is a hypernym of by-election; that is, election is a word with a broader meaning than by-election:

by-election (noun)	election (noun)
a special election between regular elections	the act of selecting someone or something; the exercise of deliberate choice
	a vote to select the winner of a position or political office
	the predestination of some individuals as objects of divine mercy (especially as conceived by Calvinists)
	the status or fact of being elected