computing machine vs computer

computing machine and computer both are nouns.

Word	Noun	Adjective	Verb	Adverb
computing machine	Yes	No	No	No
computer	Yes	No	No	No

As nouns, computing machine and computer are synonyms defined as:

computing machine and computer: a machine for performing calculations automatically

Other synonyms of computing machine include computing device, data processor, electronic computer, information processing system.

computing machine (noun)	computer (noun)
a machine for performing calculations automatically	a machine for performing calculations automatically
	an expert at calculation (or at operating calculating machines)