But let's say you're taking a brisk walk. You can say "Let's stop for a bit and take a rest." You wouldn't say "get some rest" in that situation. "Get some rest" is more like "lie down" or at least, sit down, perhaps with your feet up.
Except perhaps as a question: "I know you were really tired yesterday after climbing that mountain. Did you get rested?" (Or, more colloquially, "Did you get rested up?" "No, I slept for nine hours but I'm still tired!"