What is the difference between homepage of website and homepage of web browser?

A home page for a website is the very first page - the landing page. So, for example, google's home page is google.com, and the home page for this site is answers.com.

A home page for a browser is the page you choose to load first when you open the browser - it can be anything you want it to be.

For example, my browser of choice is FireFox. FireFox by default has it's home page set to mozilla.com, so every time I open FireFox it opens on mozilla.com. If I want to, I can change this to open google.com when FireFox opens.

You can find out how to change your browser's home page by visiting your favorite browser's website and looking up the instructions.