There are several approaches to creating a mobile-friendly web presence. They are usually divided into three ‘types’, each of which provides a different experience for mobile users:
Responsive: the page - URL, HTML, images, everything - remains the same, but the CSS gives different rules based on browser width.
RESS/Adaptive/Dynamic Serving: the URL remains the same, but the server sends different HTML and CSS based on what type of device is requesting the page.
Separate Mobile Site: usually hosted on a subdomain (e.g. m.domain.com) or sometimes a subfolder (e.g. www.domain.com/mobile), but it can also use the same URLs as the desktop site, and simply serve different HTML (called dynamic serving) to desktop and mobile visitors based on user agent.
If the mobile site uses different URLs, they are often kept parallel with their desktop counterparts (e.g. www.domain.com/first-page and m.domain.com/first-page), which allows for smooth redirects based on user agent. But since it’s a separate set of pages, the options are unlimited. You could choose to have a completely different site structure, in which case the mobile URLs might be necessarily different.