Right. For fast action, you want a fast shutter speed so the movement won't get blurred. Conversely, if you want to capture motion, then you would use a slower shutter speed. I'll define by example:
I used a fast shutter speed - maybe 1/4000th of a second - to freeze the tennis ball as it came off the racquet.
Whereas:
Here I used a 1/8th second exposure to blur the passing scenery and show a sense of speed.
There is a useful guideline for the minimum shutter speed that will let you capture steady handheld images without the effects of camera shake - take your focal length and use it as the shutter speed. For example, the average photographer could hand-hold your 50mm lens at about 1/60th with no camera shake, but would need to shoot at least 1/320th with a 300mm lens. This is because longer lenses amplify the effects of even the slightest tremble.