The AK-12 is an assault rifle chambered for the 5.45x39mm cartridge, while the AK-15 is chambered for the 7.62x39mm. Both rifles are manufactured by Kalashnikov and the AK-12 in particular was adopted as the main service rifle for the Russian army.
The AK-12 simply represents the latest iteration of the AK-series of rifles. It began development in 2011 under the company Izhmash, which later developed into Kalashnikov. Later, Izhmash would develop into the company Kalashnikov (a Russian company separate from Kalashnikov USA in the United States).
The AK-12 is a selective fire rifle with fully automatic, two round burst, and semi-automatic modes. It is designed to be more advanced and cheaper to build than previous versions of the AK rifle. It features a gas operated, long stroke piston system, a rotating bolt, and a Picatinny rail over the dust cover for adding optics such as red dot sights, magnifiers, and scopes, and another picatinny rail under the handguard for adding flashlights, lasers, or vertical fore grips. The rifle is also designed to be fitted with a bayonet, a grenade launcher (specifically the GP25 under barrel grenade launcher) and suppressor.
The AK-12 also has a cyclic rate of fire of seven hundred rounds a minute, which is a hundred rounds per minute faster than previous versions of the AK rifle.
The AK-12 and the AK-15 are also identical, with the only differences being the difference in calibers as noted above.