The answer for question might sound simple. A web design company designs websites, yes it is logical, and that is what a web design company generally does, but the answer is more than it. To convert your concept and build a successful website around it, is not a piece of cake.
There are different web design companies and usually, they offer a wide range of other services as well except just website designing, but in most cases they specialize in a particular type of website design or in a specific segment (niche). For example, web design company “A” specialize in websites of small business and others company “B” focus only on websites of large corporations, or large companies within a specific segment for e.g. automotive, hair salons, etc. There are not any specific set of rules for the type of website a web design company can get involved with.
While searching a web design companies for your project you should find out what resources the company have to build your website. If you need a site with multiple users to manage and manage an entire database from admin area then most probably you need a CMS or a web development specialist who can code in PHP or ASP (this option will cost you more). If you have a Windows based server then you will need a web designer who can operate within Windows environment.