Yeah, a Live Tile is a widget, but it's a well integrated widget. It's an application shortcut that displays information while still looking like an application shortcut. Widgets are completely separate, visually. Windows Live Tiles don't need to be specifically added, if you add an app shortcut to your start screen it's automatically also a widget that looks visually consistent with the rest of the OS.

Your assessment is not too far off. Live Tiles is a more elegant way of handling widgets.

Sort of, I guess the biggest difference is in how you add them. Adding widgets is an intentional thing; you decide you want a weather widget on your screen. A tile is something you discover and decide to keep for later. So you find a restaurant you like, you pin it. You don't say "I want to pin something, let me look through a list of pinnable things and pick one".

That's one use for Tiles, but not the one I'm referring to. Pinning a map is great, but pinning a weather app makes it continuously update the local weather and forecast right on the app shortcut. Pinning a stock app makes your stock quotes show up right there on the app shortcut. There's many use cases for pinning a Live Tile, and the best part is they're all done using the same mechanism.

To do something like this on Android, you'd need an API for an app to install a widget. I don't know if that's possible outside of the standard appstore download/install process.