What are the differences between IE and, ehm, IE?

I notice that there are very big differences between starting up IE from the desktop taskbar and starting it up from the Windows 8.1 start screen. Doing so results in a remarkably dissimilar user experience.

For instance, the IE started up from the start screen has fewer options (no menu bar, no F12 etc). It behaves like a totally different program. Also, the icons shown in the Alt+Tab display are different.

In fact, when I first noticed this, I thought maybe Microsoft had perhaps installed Edge on my machine. But no, both versions identify themselves as Inteet Explorer 11.

So, why this difference? Why does the same program behave in such different ways depending on how it is started up? Am I missing something?