babysitting vs baby sitting

babysitting and baby sitting both are nouns.

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

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

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

babysitting (noun)	baby sitting (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