There always has to be a web page to "anchor" the applet, but you can make it open a new window using AWT or Swing. This window is usually prominently marked as being a Java Applet Window so you can't do something evil such as make a bogus web browser window and prompt for a password (such things have been known to happen, alas). The anchor point can be fairly small, but the browser usually forbids it from being totally invisible - once again, they're trying to make sure the user isn't being tricked. The two primary distinguishing features of applets are, first, that they must run in a container (such as a web browser) and two, that they run in a feature-restricted environment (sandbox).
Customer surveys are for companies who didn't pay proper attention to begin with.