debate vs argue

debate is a noun but argue is not a noun.

Word	Noun	Adjective	Verb	Adverb
debate	Yes	No	Yes	No
argue	No	No	Yes	No

As verbs, debate and argue are synonyms defined as:

Other synonyms of debate include contend, fence.

debate (noun)	argue (noun)
the formal presentation of a stated proposition and the opposition to it (usually followed by a vote)
a discussion in which reasons are advanced for and against some proposition or proposal

debate (verb)	argue (verb)
argue with one another	have an argument about something
discuss the pros and cons of an issue	give evidence of
have an argument about something	present reasons and arguments
think about carefully; weigh