Here is an excerpt from Grant Palmer's massive Java Programmer's Reference:
The classes contained in the java.awt package provide a basic capability to create graphical user interfaces, but the scope of the tools contained in java.awt is limited. Furthermore, the actual implementation of the components is done in a language other than Java, and the look and behavior of the components is somewhat dependent on the runtime platform's native environment. AWT components might act slightly differently on a UNIX system than they would on a PC.
The Swing classes are the next-generation (Java 2) GUI classes. They provide a number of new components including trees, tables, and tooltips, etc. Swing components are written entirely in Java...
Does this help? If you don't have his reference, at least take a look at it. You probably won't need another for some time. It runs about $35 and contains over 1200 pages of solid examples and references.