The general point is the same: the pros perceive the board differently, because they see the emergent patterns. My contention is that this is the heart of intuition (or at least an important subset of intuition).
The advantage of training with an AI is that the AI will happily play you for ten or twelve hours a day, from any position you please, without tiring; you can ask it for the evaluation of any position, and it will generally provide an extremely accurate one; it will immediately reveal errors in your calculations and suggest tactical possibilities that few humans would see; and it will play perfect (for small sets of pieces) and near-perfect endgames against you.
Last, but not least, computer chess databases are like nothing available 20 years ago. Chess professionals (and amateurs) have access to all the games they have ever played, hundreds of games played by any potential rival, and hundreds or thousands of games played by IMs and GMs in any potential opening line.
Yeah, you're probably right. I had also forgotten about those chess databases, those are quite powerful. The problem is probably that the last commercial chess AI I used dates from ~1995, when they weren't that smart yet. Or, more accurately, the computers didn't have enough computing power to be strong and at the same time take a reasonable amount of time before playing.
They also misplaced groups of pieces instead individual pieces in meaningful positions.
Make perfect sense with pattern matching, pros obviously think in terms of patterns more than amateurs.
But this is still far from knowing in any significant detail how pro think in patterns.