in the south vs to the south

in the south and to the south both are adverbs.

Word	Noun	Adjective	Verb	Adverb
in the south	No	No	No	Yes
to the south	No	No	No	Yes

As adverbs, in the south and to the south are synonyms defined as:

Other synonyms of in the south include south.

in the south (adverb)	to the south (adverb)
in a southern direction	in a southern direction