A website with device detection can identify the type of device attempting to gain access and can use that information to serve an alternative version of the content. This is most commonly used for sites with a separate mobile version.
A website with a mobile version is different to a responsive website. A responsive website has one version which can scale depending on the width of the device or browser.
Dedicated mobile sites are popular for sites which require more user interaction as you can tailor the site specifically for mobile users. Even the content you serve may need to be optimised for mobile, not just the presentation and styling.
Mashable discuss the different approaches in the article Should You Build a Responsive Site or a Native Mobile App?
You can use the synchronisation tool in Contensis to repurpose content for a mobile website. Using synchronisation, you can have a piece of content in use on both your desktop and mobile site, but only need to edit it once.