It may depend on the issuer, but generally a "business" card (a) requires you to state that you are a business of some sort and are using the card for business expenses (you can state that you are a sole proprietorship and doing business in your own name, though), and (b) permits a number of sub-cards to be issued to your "employees" all of which are accounted for through your "main" business card account.

In other words, a bit more hassle, and for a one-person business a bit more trouble. And, of course, for someone who wants to keep the accounts separate but not solely for business purposes, the "business" card wouldn't do the trick (unless the user is less than candid with the issuer).