The full idiom is "graceful degradation". It's been common on the web since the 90s, but I think it actually came from networking jargon.
It's not the same as responsive design. Graceful degradation implies a sort of hierarchy, where you subtract features on platforms that don't support them. So if you're using an supercool advanced browser feature, like colored text, you don't break the site for older browsers.
The responsive design idea is really more about different use cases than adapting to a more primitive environment.
I'm actually disagreeing with what you are saying: responsive design is such a poor solution to the problem of providing a mobile or tablet site, that it is actually more accurate to refer to it as graceful degradation, rather than as addressing a new use case.
It's not the same as responsive design. Graceful degradation implies a sort of hierarchy, where you subtract features on platforms that don't support them. So if you're using an supercool advanced browser feature, like colored text, you don't break the site for older browsers.
The responsive design idea is really more about different use cases than adapting to a more primitive environment.