The differentiator, it seems, lies in the number of users you’d like to authorize. According to Microsoft’s pricing page, here are the maximum number of users you can sign up for various Office 365 for Business options:
Office 365 Small Business and Small Business Premium: 25 users
Office 365 MidSize Business: 300 users
Office 365 Enterprise E1 and E3: Unlimited users
The Small Business option offers no desktop applications to install and no mobile app options. Nor does the Enterprise E1 option, though it serves an unlimited number of users, while the Small Business plan is limited to just 25.