beyond doubt vs beyond a shadow of a doubt

beyond doubt is an adjective but beyond a shadow of a doubt is not an adjective.

Word	Noun	Adjective	Verb	Adverb
beyond doubt	No	Yes	No	Yes
beyond a shadow of a doubt	No	No	No	Yes

As adverbs, beyond doubt and beyond a shadow of a doubt are synonyms defined as:

beyond doubt and beyond a shadow of a doubt: in a manner or to a degree that could not be doubted

Other synonyms of beyond doubt include beyond a doubt, indubitably.

beyond doubt (adjective)	beyond a shadow of a doubt (adjective)
too obvious to be doubted

beyond doubt (adverb)	beyond a shadow of a doubt (adverb)
in a manner or to a degree that could not be doubted	in a manner or to a degree that could not be doubted