Heavy and light components
Most of the issues related to mixing AWT and Swing components are related to the mixing of so-called heavyweight and lightweight components. A heavyweight component is one that is associated with its own native screen resource (commonly known as a peer). A lightweight component is one that "borrows" the screen resource of an ancestor (which means it has no native resource of its own -- so it's "lighter").
(Lightweight component support was introduced in JDK1.1, and you can read more about it in the JDK1.1 Lightweight UI Framework design document.)