how do microwaves and radiation relate to each other?

Microwaves are radiation. They are a small part of the electromagnetic spectrum between 300 MHz (0.3 GHz) and 300 GHz.

If you are being lazy and really mean microwave ovens: then these operate by spraying the food inside the chamber with microwave radiation. This heats the water which is always within, or around, the product and so cooks it.

Microwaves are electro magnetic waves of very large wave length and radiations are electromagnetic waves of very small wave length.