The difference of a website and web application is detremined mainly by the capabilties...

A website provides information, much like a brochure except is published online and accessible to the world via the web address. Websites are incapable of interacting with your site visitors and can only serve one purpose and that is to provide them with information the only funational capability of a website is to email a form on the site. 

A web application is much more robust and its possibilities are limitless. Some examples of web applications are facebook, google, youtube,etc.  Web applications can not only identify your site visitors but can interact with them accordingly. Web applications typically requires a database and functional programming that will allow for the site to communicate with the database.

It is important to determine if your seeking a website or web application. This is what I have noticed, web designers typically are limited to website(front-end HTML,CSS and if there good Javascript) development. So if you are seeking to develop a web application I personally would avoid Web Designers (or confirm that the designer is able to program) and instead seek out specifically Web Programmers or Web Application Developers. The majority of Web Programmers started out in basic web design so they are capable of doing both.  

I typically provide my clients seeking a website with some do-it yourself options, that they may not be aware. Website projects are quite basic for me, and require a couple of hours of work. I think Costco offers a 5 page website for $500, I don't quite charge that much, therefore you probably should pay more than that if your looking for a simple website.