to a higher place vs above

to a higher place is not a noun while above is a noun.

Word	Noun	Adjective	Verb	Adverb
to a higher place	No	No	No	Yes
above	Yes	Yes	No	Yes

As adverbs, to a higher place and above are synonyms defined as:

Other synonyms of to a higher place include higher up, in a higher place.

to a higher place (noun)	above (noun)
	an earlier section of a written text

to a higher place (adjective)	above (adjective)
	appearing earlier in the same text

to a higher place (adverb)	above (adverb)
in or to a place that is higher	(in writing) at an earlier place
	in or to a place that is higher