to that degree vs to that extent

to that degree and to that extent both are adverbs.

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

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

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

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