They're totally different. A "web page" is HTML -- marked-up text which is displayed in a web browser. It fills a whole brower window. Writing HTML isn't generally considered programming, although a lot of HTML is created by writing code which in turn creates the HTML.
An "applet" is Java code with a GUI, and which can appear embedded inside a web page -- it takes up part of a window. Writing an applet in Java is, definitely, programming.