guesstimate vs approximation

guesstimate and approximation both are nouns.

Word	Noun	Adjective	Verb	Adverb
guesstimate	Yes	No	Yes	No
approximation	Yes	No	No	No

As nouns, approximation is a hypernym of guesstimate; that is, approximation is a word with a broader meaning than guesstimate:

Other hypernyms of guesstimate include estimate, estimation, idea.

guesstimate (noun)	approximation (noun)
an estimate that combines reasoning with guessing	the act of bringing near or bringing together especially the cut edges of tissue
	the quality of coming near to identity (especially close in quantity)
	an approximate calculation of quantity or degree or worth
	an imprecise or incomplete account

guesstimate (verb)	approximation (verb)
estimate based on a calculation