Here's a breakdown:
* Earth's Crust: This is the outermost layer of the Earth, what we walk on. It's relatively thin compared to the other layers.
* Earth's Mantle: This is a thick layer of mostly solid rock that lies beneath the crust. It's hot and under immense pressure, and it behaves like a very viscous fluid over long periods of time.
* Tectonic Plates: These are pieces of the Earth's lithosphere (which includes the crust and the uppermost part of the mantle) that move around on top of the asthenosphere (the semi-molten part of the upper mantle).
So, the plates themselves are part of the crust and the upper mantle, but they "float" on the softer, partially molten asthenosphere within the mantle.