In the Office 365 world Groups are everything. Groups are a shared mailbox and a sharepoint site w/ document library. All permissions are determined by permission to the mailbox. "Integration with Office" means integration with Exchange, Sharepoint, Lync more than it means integration with Excel, Word etc.
A team exists inside a group. When a file is uploaded, it really uploads to sharepoint/onedrive. Each Channel creates a new folder inside the sharepoint document library.
What teams really is is a new skin over the top of sharepoint/skypelync/exchange. You have most of the same features you had in the "older" (last years new) Groups interface, plus you have a persistent chat that skype is missing. A bunch of the buttons are rearranged slightly from groups.
Whats somewhat frustrating is how features and buttons are duplicated three times between a Team, a Group, and a Yammer group. You really need strong organizational policy to standardize behavior, or you will end up with chaos. It's somewhat that obvious Microsoft is trying to converge these three products until they are 100% feature complete, and then merge them into one thing. Groups are a near Yammer clone built on top of Sharepoint/Exchange, and Teams are basically the same thing, but drawn to look like Slack.