You can put a pistol caliber or .223 Remington cartridge length upper on an AR-15 and a .308 Winchester cartridge length upper on an AR-10. But you can't put an AR-10 upper on an AR-15 lower or vise vesra.
.22 Long Rifle, 7.62x25mm, 9mm Luger, 40 S&W, 10mm, 45 ACP, .50 AE, .17 Remington, .204 Ruger, 5.45x39mm, .222 Remington, .223 Remington, 5.56x45mm NATO, .223 WSSM, 6mm PPC, 6mm-223 Remington (6x45mm), .243 WSSM, .25 WSSM, 6.5 Grendell, 6.8 SPC, .300 Whisper, 7.62x39mm, .450 Bushmaster, .45 Professional, .458 SOCOM, .499 LWRC, .50 Beowulf, and the .50 BMG bolt-action are just some of the uppers that will fit an AR-15 lower without modification. The pistol calibers have mag-well adaptors that pop in. Everything else is good to go as is.
AR-10s can use any caliber based on .308 Winchester length cartrigdes based on .308 and .284 Wichester as well as some big fat non-belted magnum cases. 6.5-.284 Winchester is just one of the wildcats available for it. Standard calibers include .243 Winchester, .260 Remington, 7mm-08 Remington, .308 Winchester/7.62x51mm, .338 Federal, and .358 Winchester. There are several dozen more possibilities including 6.5mm Creedmoor.