Savage = Do it yourself
Even though I don't own a Savage, I came close. During my research, I believe I stumbled over the answer to this question.
(You may need to look up "Headspace" in the THR Library)
For a conventional rifle (Winchester, Remington, etc.) the barrel is threaded to match and then screwed into the end of the receiver, torqued correctly, then the chamber (which was cut deliberately short) is reamed to length for correct headspace. This all requires a lot of tools, and usually the services of a gunsmith (unless you are a machinist...)
For a Savage, the barrel is attached to the threaded receiver with a barrel lock nut. Basically, the barrel can be adjusted until headspace gauges show you have the correct headspace. No machine work. This is handy not only for changing calibers, but for replacing a worn-out barrel in the same caliber.
Provided the action length is the same (such as .308 and .243) and the bolt face is the same, changing calibers can be as simple as changing barrels. I believe you can get into magazine feed problems if you get too far afield in cartridge dimensions.
Someone who has actually done a Savage barrel change may have a better explanation, but I think what I've related is the heart of the matter.