shorthand vs script

shorthand and script both are nouns.

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

As nouns, script is a hypernym of shorthand; that is, script is a word with a broader meaning than shorthand:

Other hypernyms of shorthand include hand, handwriting.

shorthand (noun)	script (noun)
a method of writing rapidly using an abbreviated symbolic system	a written version of a play or other dramatic composition; used in preparing for a performance
	a particular orthography or writing system
	something written by hand

shorthand (adjective)	script (adjective)
written in abbreviated or symbolic form

shorthand (verb)	script (verb)
	write a script for