order vs arrange

order is a noun but arrange is not a noun.

Word	Noun	Adjective	Verb	Adverb
order	Yes	No	Yes	No
arrange	No	No	Yes	No

As verbs, arrange is a hypernym of order; that is, arrange is a word with a broader meaning than order:

Other hypernyms of order include set up.

As verbs, arrange is a hypernym of order; that is, arrange is a word with a broader meaning than order:

Other hypernyms of order include set up.

As verbs, order and arrange are synonyms defined as:

Other synonyms of order include put, set up.

order (noun)	arrange (noun)
the act of putting things in a sequential arrangement
(architecture) one of original three styles of Greek architecture distinguished by the type of column and entablature used or a style developed from the original three by the Romans
a degree in a continuum of size or quantity
a legally binding command or decision entered on the court record (as if issued by a court or judge)
a commercial document used to request someone to supply something in return for payment and providing specifications and quantities
a body of rules followed by an assembly
(often plural) a command given by a superior (e.g., a military or law enforcement officer) that must be obeyed
a request for something to be made, supplied, or served
logical or comprehensible arrangement of separate elements
(biology) taxonomic group containing one or more families
a formal association of people with similar interests
a group of person living under a religious rule
established customary state (especially of society)
a condition of regular or proper arrangement

order (verb)	arrange (verb)
bring order to or into	arrange attractively
place in a certain order	arrange thoughts, ideas, temporal events
assign a rank or rating to	make arrangements for
arrange thoughts, ideas, temporal events	put into a proper or systematic order
make a request for something	adapt for performance in a different way
give instructions to or direct somebody to do something with authority	set (printed matter) into a specific format
issue commands or orders for	plan, organize, and carry out (an event)
bring into conformity with rules or principles or usage; impose regulations
appoint to a clerical posts