The steel core ammo uses a mild, not hardened steel core. Yes, it's consideered "armor piercing" although it probably won't go through the side of a Bradley or anything like that.
IIRC, it's only handgun ammo that is restricted as far as AP ammo goes (it's really a restriction on what percentage of the core can be of which materials. Some rifle cartridges (like .308) are also restricted, because they can be fired from handguns such as the T/C Encore, and the ATF considers them handgun rounds. . .go figure.
If you're talking 7.62x54R, it's no problem, there's a lot of steel core ammo out there (it's cheaper to produce than lead-core), mostly shoots well. The only downside is that some ranges won't let you fire it there.