Both terms are often used interchangeably and the distinction has become fuzzy over time. But there are some key differences between both of them

• Most application servers have a web server in their core. But application servers also come with other features such as connection pooling, message queues etc. This is not a part of web servers.
• A web server is designed to serve HTTP content while an application server can do much more. It can also serve content over RPC/RMI.
• Although web servers were initially designed to serve only static content such as images and javascript files, these days, most web servers have plugins that allow them to serve dynamic content using PHP, Perl etc. Application servers were always intended to serve dynamic content and carried the business logic for enterprises.

That being said, often you can use one or the other to serve your content. But, when people quote web servers, they generally think of HTTP protocols and UI content. When they quote application servers, they generally think of heavy business logic with message queues, beans, distributed computing etc.