Would they actually –and really – calculate 20 moves ahead, they surely would then play 20 moves very fast. This is not the case. They usually play one move at the time, only openings (no calculations needed) or various exchanges (maybe 3 moves) they play fast.
So, usually, they calculate one move ahead.
ps. I don’t know, but this is logical?
There are two points where a world class player might go into a long think. One being if they've reached a critical position or otherwise need to find the thread (theme, idea) of the game. The other is when the position is very tactical in nature and has many forcing moves. Although recaptures are not the only time a move is the only move, recaptures are a good example. You're somewhat right that after these thinks the moves do come faster, at least comparatively.
However other than this, like Tonaydal said, you don't quite hit the nail on the head.
First of all, calculating 20 moves isn't the same as looking into a crystal ball -- it's not possible to see every variation, you just try to find the best moves for you opponent to work against your ideas. If your opponent has a particularly dangerous way to work against you, and you're a world class player, (and there are some forcing lines e.g. re-captures) then 20 moves is not impractical or impossible, and yes it happens, even every day.
To the amateur each move is made in isolation, one at a time, therefore each move gets equal amount of calculation. To a world class player all the moves are connected and flow in a logical order. This is one reason they remember games from 10 years ago, not because of photographic memories, most of them do not have this, it's just like you can remember the plot of a 2 hour movie a week, month, or even years after going to the theaters, because the information has order and flows logically from beginning to end.
They don't bang out those 20 moves because the opponent might find a slightly different way to challenge the idea that suites their playing style -- as long as this different way doesn't change the theme though, the following calculation will not take nearly as long as the initial deep think.
sorry was down pub havin' Sunday lunch, didn't get to see your post, tiresomebug ,but that was the way the story was reported when I read it nearly 40 years ago; and the story is extremely aposite to the OP's question - or don't they do lateral thinking in Singapore either ?