publically vs in public

publically and in public both are adverbs.

Word	Noun	Adjective	Verb	Adverb
publically	No	No	No	Yes
in public	No	No	No	Yes

As adverbs, publically and in public are synonyms defined as:

publically and in public: in a manner accessible to or observable by the public; openly

Other synonyms of publically include publicly.

publically (adverb)	in public (adverb)
in a manner accessible to or observable by the public; openly	in a manner accessible to or observable by the public; openly