to that extent vs to that degree

to that extent and to that degree both are adverbs.

Word	Noun	Adjective	Verb	Adverb
to that extent	No	No	No	Yes
to that degree	No	No	No	Yes

As adverbs, to that extent and to that degree are synonyms defined as:

Other synonyms of to that extent include in so far, insofar, so far.

to that extent (adverb)	to that degree (adverb)
to the degree or extent that	to the degree or extent that