cursive script vs running hand

cursive script and running hand both are nouns.

Word	Noun	Adjective	Verb	Adverb
cursive script	Yes	No	No	No
running hand	Yes	No	No	No

As nouns, cursive script and running hand are synonyms defined as:

cursive script and running hand: rapid handwriting in which letters are set down in full and are cursively connected within words without lifting the writing implement from the paper

Other synonyms of cursive script include cursive, longhand.

cursive script (noun)	running hand (noun)
rapid handwriting in which letters are set down in full and are cursively connected within words without lifting the writing implement from the paper	rapid handwriting in which letters are set down in full and are cursively connected within words without lifting the writing implement from the paper