Fluid Design means that different sections of the site are defined relatively (eg, an element is 50% of the page width). No matter what browser you're using: Smartphone, Tablet, Desktop, the site will look (mostly) the same and have the same proportions (this element will take up half the screen). This is because in your CSS, everything is defined in terms of percent, or ems, or some other metric that scales nicely from device to device (Whereas defining fixed sizes in pixels might make and element take up half the screen on a desktop, the whole screen on a tablet, and be bigger than the screen on a smartphone).
Responsive design is usually more on the programming side, where you detect the user's browser (via useragent) or the size of their screen, and actually show them a different view based on the size of their device. For example, you might use a three column layout for desktops, a two column layout for tablets, and a single column layout on smartphones. In this case, the view on each device looks very different, because you are actually changing the view based on the device.
Twitter Bootstrap can do both of these, and they have some nice examples on their site: