taxicab vs cab

taxicab and cab both are nouns.

Word	Noun	Adjective	Verb	Adverb
taxicab	Yes	No	No	No
cab	Yes	No	Yes	No

As nouns, taxicab and cab are synonyms defined as:

taxicab and cab: a car driven by a person whose job is to take passengers where they want to go in exchange for money

Other synonyms of taxicab include hack, taxi.

taxicab (noun)	cab (noun)
a car driven by a person whose job is to take passengers where they want to go in exchange for money	a car driven by a person whose job is to take passengers where they want to go in exchange for money
	small two-wheeled horse-drawn carriage; with two seats and a folding hood
	a compartment at the front of a motor vehicle or locomotive where driver sits

taxicab (verb)	cab (verb)
	ride in a taxicab