The difference is that if all you have is a radar telling you that something is moving at 20mph then you can guess that it's probably a vehicle in the road and you should brake. But if there's something that's stationary at 0 mph it might very well be an overhead sign or otherwise something that you don't have to avoid. A radar can be very precise in detecting distance and relative velocity but very bad at detecting which direction something is in. For the sort of non-dish radars used in cars I'm not even sure they can detect direction at all.
Ignoring things that aren't moving is a standard technique in radar to prevent your returns from being swamped by, e.g., the ground instead of fast moving planes you're looking for.
To add even more detail, as there still appears to be a lot of confusion:
The radar systems in these vehicles send out a radio pulse in a broad approximate-cone forward. They get bounces back from everything that reflects radio in front of them. Distance from the object is calculated by time between pulse and response. Speed towards/away from the object is calculated from Doppler shift of the radio frequency.
There are two main things that these systems can't detect.
1. Speed of the object perpendicular to the direction of radio wave travel.
2. Location of the object within the approximate-cone the radio pulse travels in.
Note that thanks to the second, you can't calculate the first with higher-level object tracking, either.
So the data you get back is a list of (same-direction velocity component, distance) pairs. There's no way to distinguish between stationary objects in the road and stationary objects above the road, to the side of the road, or even the surface of the road itself.
Radar just doesn't provide the directional information necessary to handle obstacle detection safely.
Ignoring things that aren't moving is a standard technique in radar to prevent your returns from being swamped by, e.g., the ground instead of fast moving planes you're looking for.