Responsive web-design is a common name for techniques which allows to display single site layout on different devices and screen sizes.
Indeed, there are more than one layout behind the scene of responsive design.
It may be a couple variants for the different screens resolutions but all of them are combined into one single layout.
Usually site has 3 different layouts ( for desktop, for tables and for the phones ) or event 2 ( for desktop and mobile devices ).
Main advantage of responsive design: you don’t need a separate theme for your site, site will fit device size automatically.
If you need a responsive site you should start to develop new design as responsive, but it also possible to make your current design responsive, if you want.
To make sure your design can be responsive or if you want a brand-new responsive layout for your site — you can always get a quote.