TL;DR: A website is a collection of pages whereas a webpage refers to only one particular page on a website.
We've been asked this regularly and decided to write down our explanation.
The difference between a "Website" and a "Webpage"
Let's take totally-nerdy.com for example. That's our website. And totally-nerdy.com/blog/ is one webpage on it. You navigate to individual pages by appending something to the website address, in this particular example it's "/blog/" which we added to the address of the website.
The address of a website (totally-nerdy.com) is generally refered to as a domain. But that's something for another day.