Hi Carol, welcome to our Files group! Here's a high level summary, glad to provide more detail as desired:

Files. "Files" in Salesforce has traditionally referred to Chatter Files, while "Content" has referred to our Content Libraries product. We're starting to unify the feature set between these two file types so that both file types have the same features. In Winter '15 for example, we're publishing a Content Deliveries API that will work for both Chatter Files and Content.

Files Sync. Files Sync is a free feature available in Unlimited, Performance, Enterprise and Chatter Plus licenses. This feature consists of a downloadable desktop app, similar to the Dropbox desktop app, that allows users to sync their desktop files and folder hierarchy into the Salesforce cloud where these synced files and folders are then available across web and mobile (Salesforce1). Synced Files are private by default but can be shared in Salesforce to persons, groups and records as desired. Here's a great video that showcases Files Sync at the beginning

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Files Connect. Files Connect is a feature that will be available in Winter '15 that integrates Microsoft Sharepoint 2010, Sharepoint 2013 and Office 365 into Salesforce.

are the product managers for Files Connect and can provide additional information on functionality and pricing & packaging.

is our marketing lead for Salesforce Files and is creating documentation with additional details about each of these Files features.

Any of my comments above regarding future functionality is "Safe Harbor" of course.