recovering vs convalescent

recovering is not a noun while convalescent is a noun.

Word	Noun	Adjective	Verb	Adverb
recovering	No	Yes	No	No
convalescent	Yes	Yes	No	No

As adjectives, recovering and convalescent are synonyms defined as:

recovering and convalescent: returning to health after illness or debility

recovering (noun)	convalescent (noun)
	a person who is recovering from illness

recovering (adjective)	convalescent (adjective)
returning to health after illness or debility	returning to health after illness or debility