longhand vs round hand

longhand and round hand both are nouns.

Word	Noun	Adjective	Verb	Adverb
longhand	Yes	Yes	No	No
round hand	Yes	No	No	No

As nouns, round hand is a hyponym of longhand; that is, round hand is a word with a more specific, narrower meaning than longhand:

longhand: rapid handwriting in which letters are set down in full and are cursively connected within words without lifting the writing implement from the paper
round hand: a clearly written style of longhand with large round curves

Other hyponyms of longhand include minuscule, copperplate, italic.

longhand (noun)	round 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	a clearly written style of longhand with large round curves

longhand (adjective)	round hand (adjective)
having words written out in full by hand