Designing a website today is completely different than just a few years ago. Your web page is read on lots of different screens. It can be PC, Mac, iPhone, Android, BlackBerry, iPad, TV or something completely different. Therefore, it is of utmost importance not to customize your web for a particular phone or computer environment. This is what Responsive design allows us to do.
So what is the difference between an app, mobile web and a web page with responsive design? A simple answer is that a page with responsive design always has only one and the same link. Say e.g. that you sell headphones and that one of your products is called "Koss Porta Pro". The address will then be www.your-company.com/headphones/coss-pro. When Google searches your page, the search engine understands that the page is about "Koss Porta Pro" and adds it to the search results.
I who google "Koss headphones" with my iPhone obviously click on the same link and are then taken to the same page, now obviously optimized for my iPhone, but it is still the same page.
If you have a regular website plus a mobile website, you have two links instead. Google values it as two separate pages that are really about the same thing, which results in the search engine disliking your page as a whole due to something they call duplicate content.
Two links also degrade the experience for the user. A mobile surfer who emails / tweets / facebooks the link spreads your mobile website even to those who sit on a big screen.
Having an app makes the information inaccessible and searchable from the web. It also requires your user to go into an App Store, search for your business, find, download, enter their password and launch the app. Compared to just entering www.your-company.com
Responsive design is about showing your page in the absolute best way for your visitors - not about creating several different websites with similar content.