putter vs monkey around

putter is a noun but monkey around is not a noun.

Word	Noun	Adjective	Verb	Adverb
putter	Yes	No	Yes	No
monkey around	No	No	Yes	No

As verbs, putter and monkey around are synonyms defined as:

putter and monkey around: do random, unplanned work or activities or spend time idly

Other synonyms of putter include mess around, monkey, muck about, muck around, potter, tinker.

putter (noun)	monkey around (noun)
the iron normally used on the putting green
a golfer who is putting

putter (verb)	monkey around (verb)
move around aimlessly	do random, unplanned work or activities or spend time idly
do random, unplanned work or activities or spend time idly
work lightly