to the south vs in the south

to the south and in the south both are adverbs.

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

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

Other synonyms of to the south include south.

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