mosquito bite vs insect bite

mosquito bite and insect bite both are nouns.

Word	Noun	Adjective	Verb	Adverb
mosquito bite	Yes	No	No	No
insect bite	Yes	No	No	No

As nouns, insect bite is a hypernym of mosquito bite; that is, insect bite is a word with a broader meaning than mosquito bite:

mosquito bite: a sting inflicted by a mosquito
insect bite: a painful wound caused by the thrust of an insect's stinger into skin

Other hypernyms of mosquito bite include bite, sting.

mosquito bite (noun)	insect bite (noun)
a sting inflicted by a mosquito	a painful wound caused by the thrust of an insect's stinger into skin