They are the same program as Outlook Express, there is no "online" component to it, it's 100% identical to the old program in every way, only with new icons and a updated "ribbon" toolbar. There's no other difference, your email is not stored "online" or any differently. The only change was some visuals.
You can still use it with POP, IMAP, or even the old Hotmail if you wanted - or of course any email provider like Comcast, Verizon, AT&T, whatever. It's exactly what Outlook Express is, only with a new icon pack.
See below. Left is Windows XP fresh install from 2002 with the original Outlook Express. Right is Windows 7 running the newest available version of Windows Essentials. If you open the source files and DLL's, you'll see most are even the same, because it is the same program.