snatch vs snatch up

snatch is a noun but snatch up is not a noun.

Word	Noun	Adjective	Verb	Adverb
snatch	Yes	No	Yes	No
snatch up	No	No	Yes	No

As verbs, snatch and snatch up are synonyms defined as:

Other synonyms of snatch include snap.

snatch (noun)	snatch up (noun)
the act of catching an object with the hands
a weightlift in which the barbell is lifted overhead in one rapid motion
(law) the unlawful act of capturing and carrying away a person against their will and holding them in false imprisonment
obscene terms for female genitals
a small fragment

snatch (verb)	snatch up (verb)
to grasp hastily or eagerly	to grasp hastily or eagerly
take away to an undisclosed location against their will and usually in order to extract a ransom
to make grasping motions