Servlets are Java based analog to CGI programs, implemented by means of a servlet container associated with an HTTP server. Servlets run on the server side. Beans are reusable code components written in Java that one can use in a variety of programming environments. JavaBeans are to Java what ActiveX controls are to Microsoft. Javabeans can run on server side, client side, within an applet etc.
So, both have nothing in common except Java.