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.