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The difference between commerce and business can be puzzling to some as the words commerce and business have a similar connotation. In a narrow sense we may get confused, say about a small stationary. but, take the case of a large company, here the term of commerce is an abstract.
Commerce is trade + aids to trade (Supporting activities such as communication, transportation, insurance, and so on)
Commerce is a part of all the activities that are carried out in the name of business such as Planning,Advertising, buying, Selling, Marketing, accounting and supervising manufacturing, etc. Commerce is just the buying and selling part of business thus being smaller in scope than business.