You are correct, the absolute best players in the world (Grandmasters) have both natural born ability and tons of training. Probably the biggest difference in my opinion is they make less mistakes. EVERY move is a good one. They tend to excel at every phase of the game not just a few and usually have no weaknesses.
Even non master players can see several moves ahead, that is a must to be a good player. They definitely can see how the game will unfold and tend to have excellent long term thinking as well as near flawless tactics.
Openings also tend to be very strong as at that level it becomes a must to learn even little nuances of openings to constantly keep up with the latest wrinkle on such and such an opening.