publicly vs in public

publicly and in public both are adverbs.

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

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

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

Other synonyms of publicly include publically.

publicly (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
by the public or the people generally