I believe the 223 dia. bullets would be for your Hornet and some of the older model 22 Jets & Fireballs, your 22-250 should be 224 dia and tho the 223 dia would pose no problems they probably wouldn't be as accurate.
A Computer lets you make more mistakes faster than any invention in human history--with the possible exception of handguns and tequila.
.224cal for 22-250, and most other modern .22cal centerfire cartridges for that matter. To my knowledge, only older production .22 Hornet rifles used .223cal bullets. But I believe that current production .22 Hornet rifles are bored for .224cal bullets.
Just out of curiousity, doesn't your reloading manual state that the 22-250 uses .224cal bullets? I'd be surprised if it didn't.
That was one of the first mistakes I made loading for my 22-250. the 223 "hornet" bullets don't work worth a dang in my 22-250. They just don't engage the lands and hit the dirt after anything over 150 yards. I cannot tell you how embarrassing that was when I was trying to show off my new Savage on prairie dogs at 400 yards. My shooting partner still finds time to bring it up in conversation.