script vs handwriting

script and handwriting both are nouns.

Word	Noun	Adjective	Verb	Adverb
script	Yes	No	Yes	No
handwriting	Yes	No	No	No

As nouns, script and handwriting are synonyms defined as:

Other synonyms of script include hand.

script (noun)	handwriting (noun)
a written version of a play or other dramatic composition; used in preparing for a performance	the activity of writing by hand
a particular orthography or writing system	something written by hand
something written by hand

script (verb)	handwriting (verb)
write a script for