I had a friend who was practicing with his new .416 for his upcoming Cape Buffalo hunt. He was using it to shoot out of his second story window at ground squirrels in his pasture. Any squirrels that he missed got new holes to hide in.
To specifically answer your question, it is my understanding that the .22-250 was originally developed as a varmint cartridge, and with the right bullets it has been successfully used on deer sized (and larger) animals. I've shot both mule deer and antelope with mine. I have friends who have shot elk and buffalo with theirs.
And the .25-05 was originally developed as a deer cartridge that would also work well on long range shots on varmints on windy days. I've used my .257 AI, which is balistically similar to the .25-06, on everything from prairie dogs to elk. It's my favorite deer, antelope, and bighorn sheep rifle.
I could see the small band of mule deer picking their way towards me through the sagebrush 800 plus yards away. With my 10 power binoculars I spotted a legal buck bringing up the tail. I dropped down and crouched behind a large chunk of sage just waiting for them to pass within range. Unfortunately, they stopped and began milling around before finally settling down, with a few of them laying down right out in the open. They were not going to come to me; if I wanted any closer, I'd...