Both the Java AppletViewer and the Java interpreter execute Java programs. The real distinction lies in the fact that the Java interpreter does nothing more than interpret Java bytecode.
The AppletViewer takes on another level of responsibility by providing a graphical framework for applets to reside in. The AppletViewer certainly must interpret Java bytecode but it also provides support for the graphical needs of applets.
Like the AppletViewer, Web browsers that support Java also have a Java interpreter built into them that is used to execute Java applets. Also like the AppletViewer, Web browsers must provide graphical support to applets.
Neither the AppletViewer nor Java-supported Web browsers are capable of running stand-alone Java applications, however.
The Java interpreter takes on this job.