twiddle vs fiddle with

twiddle is a noun but fiddle with is not a noun.

Word	Noun	Adjective	Verb	Adverb
twiddle	Yes	No	Yes	No
fiddle with	No	No	Yes	No

As verbs, twiddle and fiddle with are synonyms defined as:

twiddle and fiddle with: manipulate, as in a nervous or unconscious manner

twiddle (noun)	fiddle with (noun)
a series of small (usually idle) twists or turns

twiddle (verb)	fiddle with (verb)
manipulate, as in a nervous or unconscious manner	manipulate, as in a nervous or unconscious manner
turn in a twisting or spinning motion