yes, those are mostly true.
5.56 and 7.62 are the military designations, in millimeters, for commercial cartridges; .223 Remington and .308 Winchester respectively. properly it would be 5.56x45 NATO and 7.62x51 NATO, though most don't bother. these cartridges are functionally identical and to most intents and purposes are functionally interchangeable, but
the exact length and pressures vary and a few guns can handle one and not the other. here are some details: http://en.wikipedia.org/wiki/.223_Remington
, the short version is some .223's shouldn't shoot 5.56 and some 7.62x51's need to be very careful with the more powerful .308 loads.
the others go back the invention of metallic cartridges, the basic form of ammunition for a long time was a (mostly) straight cylinder capped at one end with a bullet and at the other with a slightly wider rim. examples: http://i73.photobucket.com/albums/i219/GrantRCanada/Cartridges/455_45sw_45colt.jpg
basically the cartridge was shoved into the chamber up to the rim to fire, and then the extractor pulled/pushed on the rim to eject. this simple design made it easy to make a more powerful version simply by making the case and chamber longer, allowing more room for powder and making sure it wouldn't fit in a gun designed for the older cartridge. ex: .22 rimfires http://www.theintermountain.com/storyPhotos/Ken's_bullets.jpg
so when you have a longer version of one of these 'straight walled' cartridges you can shoot any of the shorter versions it was based on, though it might not cycle through the action.
a few off the top of my head:
.44 magnum > .44 special >.44 russian
.357 magnum > .38 special
.327 federal magnum > .32 H&R magnum > .32 S&W long > .32 S&W
45-120 > 45-110 > 45-90 > 45-70
.22 long rifle > .22 long > .22 short
12ga 3.5'' > 12ga 3'' > 12ga 2 3/4''
20ga 3'' > 20ga 2.75'' > 20ga 2.5''
now assuming that made any sense, let's go back to your original question and expand on it. are you looking to have a gun that's more versatile, one that has a wider selection of ammunition or both?
the trouble with most of these combinations is that only one (or none) from each group is common, with the exception of .38/.357 and the shotgun shells, so it doesn't help much with ammo availability.
if you have a revolver to go with it a carbine in .357 or .44 mag is pretty neat, but the best answer to your question might not be a rifle at all but a shotgun in 12 or 20. very common in all sorts of flavors, and the different types of shells give it a great deal of versatility (birdshot, buckshot, slugs etc.)