putter vs putter around

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

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

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

Other synonyms of putter include potter, potter around.

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

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