business enterprise vs commerce

business enterprise and commerce both are nouns.

Word	Noun	Adjective	Verb	Adverb
business enterprise	Yes	No	No	No
commerce	Yes	No	No	No

As nouns, commerce is a hypernym of business enterprise; that is, commerce is a word with a broader meaning than business enterprise:

business enterprise: the activity of providing goods and services involving financial and commercial and industrial aspects
commerce: transactions (sales and purchases) having the objective of supplying commodities (goods and services)

Other hypernyms of business enterprise include commercialism, mercantilism.

business enterprise (noun)	commerce (noun)
the activity of providing goods and services involving financial and commercial and industrial aspects	transactions (sales and purchases) having the objective of supplying commodities (goods and services)
	social exchange, especially of opinions, attitudes, etc.