Do I need to have different URLs for my mobile site and the actual site?
There are three different possibilities; either you keep the URL the same for the mobile and desktop; or different URLs for both. If you use the same URL for your mobile, you can implement the responsive design or the dynamic serving. The former basically serves the same page with the same content, but changes the layout accordingly to the screen size or device. Although dynamic serving uses one URL as well, the page can show completely different content according to the device. The last possibility is implementing mobile URLs, typically at a ‘m.’ domain. Read more about it here.