averting vs turning away

averting and turning away both are nouns.

Word	Noun	Adjective	Verb	Adverb
averting	Yes	No	No	No
turning away	Yes	No	No	No

As nouns, turning away is a hypernym of averting; that is, turning away is a word with a broader meaning than averting:

averting: the act of turning yourself (or your gaze) away
turning away: deliberately avoiding; keeping away from or preventing from happening

Other hypernyms of averting include avoidance, dodging, shunning.

averting (noun)	turning away (noun)
the act of preventing something from occurring	deliberately avoiding; keeping away from or preventing from happening
the act of turning yourself (or your gaze) away