I believe that there are two differnces between scopes designed for heavy recoiling centerfire rifles and the rimfires.
First they usually don't have to be as ruggedly recoil resistant as a rifle firing a 30-06.
Second is the matter of parallax. The practical implication of parallax is that the reticle and the image are sharply focussed together.
In a centerfire rifle scope the parallax is often set at 100 to 150 yards and beyond. That means you will see your target clearly when at a longer range. This can be a problem if you are shooting at a close target, say 25 to 50 yards. The reticle will be sharp, but the image blurred. You can adjust focus for the image, but the reticle will be then blurry. Initially I had a very nice Leupold scope (from my 30-06) mounted on my 22 rifle. I could see great at 100, but close targets were tough.
In a rimfire scope the parallax is set for shorter range which is more appropriate for the distances one normally shoots a 22.
The best of both worlds comes with the Adjustable Objective (AO) scopes. I think Leupold calls it their EFR (extend focal range) scope. They AO scopes cost a bit more, but are really worth it. I just bought the Weaver Classic AO rimfire scope 3-9x. The difference is like night and day. There is a focus ring on the far (objective lens) end of the scope and will bring the target into tack sharp focus at any distance from 10 yards to infinity. At 3x it doesn't make that much difference, but you can REALLY tell the difference at higher magnifications.
Tom