QuickBooks Online Edition is the web-based/online accounting software solution offered by Intuit.
On the other hand, QuickBooks Hosting Program refers to a legally approved distribution & licensing program. Under this program, a hosting service provider is allowed to install and manage the desktop versions of QuickBooks for Windows for end users. QuickBooks Pro, Premier and Enterprise are the three versions supported for hosting under this.
In order to access the QuickBooks desktop software, the user needs to log into the service provider's server by entering a valid username and password.