What is the diffrent between flat design and ?responsive web design

Flat design can not be compared with Responsive design.

Flat design should be compared with Skeuomorphism. Apple used it a lot in the past, I am not an avid apple user but I think they also moved to flat design. Here is the picture (I did added picture here but for some reason they aren't displayed here, though just search for Apple Skeuomorphism and Flat Design).

Non Flat Designs are: 

• Reality is mimicked as close as possible by the use of gradients, drop shadow, rounded corners
• If you press a button you would feel it (virtually though) as it's pressed, as the shadow around it will vanish.

Flat Design are the one:

• Microsoft gave it great importance with the advent of Windows8
• Normally there are no gradients, shadows, rounded corner, text-shadows unless there is a good reason.
• Flat solid colors with sharp edges.

well if I assume flate design to fix pixel design or device dependent design then the design is in fixed pixel layout based on device resolution ex.900px,1024 etc.

Other hand responsive design is device independent means can fit in according to any device like iphone, ipad, tablets, laptop, desktop etc this concept came into existence when web is extended to multiple device with various resolution.

The layout that is designed for a specific screen size like windows or a mobile etc is known as flat design while the responsive web design can adjust itself automatically according to any screen size.