Yeah, that's basically the gist of it, jacket a hard, dense penetrator in a softer metal so it doesn't damage the barrel

But there's some edge cases like with m855 "green tip" 5.56 ammo which has a steel core inside a lead bullet and copper jacket, but generally isn't considered "armor piercing" even though it does penetrate armor slightly better than most other standard 5.56 rounds

So I'm gonna hedge me bets and say there may be a case where a tungsten bullet may not be considered armor piercing but I don't know the specifics of where that line would be drawn.