Technically speaking, "Windows Explorer" is also your desktop itself. (If "explorer.exe" locks up and has to restart, you'll see your desktop redraw, and occasionally your system tray icons will go missing.)
Back in the Netscape vs IE days, MS went as far as possible to "integrate" IE into the Windows OS itself, using shared DLLs, etc. This was because they were being sued and by tying it in, claimed that they couldn't
possibly remove it like the court wanted. (This was easily disproved by a very handy hack called 98lite. MS also managed to get off with the lightest of wrist-slaps, and similarly, a few years later, the Justice Dep't had them on the ropes until the Bush administration came into power and quickly let the case die due to their "pro-business" policies.) This also meant that they did dumb things like "web view" which would treat your desktop as a web page or your Windows Explorer views as web pages, hence you'd be running some amalgam of WE and IE at once - "web view" stunk and most people turned it off though. That was in Win98 and WinME, since then they're improved it and it's not quite as painful and certainly not as annoying, though they'd still be much better off completely separating IE from the OS.
But generally speaking, "Windows Explorer" is understood to be the file browser and "Internet Explorer" is the web browser, which you shouldn't use because Firefox is so much better.
And that's your little history/tech lesson for this evening. There'll be a quiz later!
