burning vs burning at the stake

burning and burning at the stake both are nouns.

Word	Noun	Adjective	Verb	Adverb
burning	Yes	Yes	No	No
burning at the stake	Yes	No	No	No

As nouns, burning and burning at the stake are synonyms defined as:

burning (noun)	burning at the stake (noun)
the act of burning something	execution by fire
execution by electricity
execution by fire
a form of torture in which cigarettes or cigars or other hot implements are used to burn the victim's skin
a process in which a substance reacts with oxygen to give heat and light
pain that feels hot as if it were on fire

burning (adjective)	burning at the stake (adjective)
of immediate import