putter vs muck about

putter is a noun but muck about is not a noun.

Word	Noun	Adjective	Verb	Adverb
putter	Yes	No	Yes	No
muck about	No	No	Yes	No

As verbs, putter and muck about are synonyms defined as:

putter and muck about: do random, unplanned work or activities or spend time idly

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

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

putter (verb)	muck about (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