[hardwired]

Is it possible to get an applet into an application frame?
Yes. Applet extends Panel, JApplet extends Applet.

Code:

class Pseudo extends JApplet {
    public void init() {

    }

    public static void main(String[] args) {
        JApplet applet = new Pseudo();
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.getContentPane().add(applet);
        f.setSize(400,400);
        f.setLocation(200,200);
        applet.init();
        // If you override start method
        // applet.start();
        f.setVisible(true);
    }
}

JButton is a Swing, lightweight component.
Button is an AWT, heavyweight component.