Hosting companies that specifically offer WordPress Hosting often times are using an optimized machine and caching system for WordPress. However, not all hosts do that, so you'll want to ask the specific host what they offer that's different about their WordPress hosting.
Any host can run WordPress, but some hosts are better optimized for it. You must ask the question at the relevant host.
We have both dedicated servers for WordPress and others for X-Cart, and others for "general" hosting. The servers are tweaked in specific sections to get the best performance out the software and user experience.