ownCloud is an open source file sharing service, which gives you control about your data. It's easy to install and run on the servers or services you choose. So you have access to your data on your own terms. It's your ownCloud.
ownCloud in a box is a fully pre-configured software appliance, which you can run on whatever system you want, physical servers, virtual servers, or in the cloud. It's based on openSUSE and built with SUSE Studio. But as a user you don't have to care. Everything comes ready to be used as your ownCloud in a box.