Yes, 222 Rem. and 223 Rem. share the same
calibre projectile, main difference is the case volume that gave the 223 the edge in velocity and performance, other diffs relate to case geometry....geometry giving the chambering advantages/disadvantages in other factors such as case life, bolt thrust, consistency in loading and accuracy potential... etc.
There are so many variants with the size (0.224inch) or very similar calibre bullet, generally the following would be classified as 22 calibre chamberings, rimmed, rimless, magnum, rimfire, handgun, liste as follows and sorted by gross case volume relative to 223Rem;

Example the Super Express vom Hofe which I mentioned elsewhere, is over twice the volume of the little(

) 223Rem. Also note the old trusty 22LR has a gross volume of 15% the 223, and uses an ever so slightly larger 225 proj.
'R' indicates the rimmed version of the chambering.
Just post any other questions around here, you can google it but the info is not always 100%, even wiki
As there are over 415 'factory' rounds, a one stop shop as far as info.... might be a bit of an ask other than a listing.