calligraphy vs script

calligraphy and script both are nouns.

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

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

Other hypernyms of calligraphy include hand, handwriting.

calligraphy (noun)	script (noun)
beautiful handwriting	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

calligraphy (verb)	script (verb)
	write a script for