baby sitting vs babysitting

baby sitting and babysitting both are nouns.

Word	Noun	Adjective	Verb	Adverb
baby sitting	Yes	No	No	No
babysitting	Yes	No	No	No

As nouns, baby sitting and babysitting are synonyms defined as:

baby sitting and babysitting: the work of a baby sitter; caring for children when their parents are not home

baby sitting (noun)	babysitting (noun)
the work of a baby sitter; caring for children when their parents are not home	the work of a baby sitter; caring for children when their parents are not home