How do masters and Grandmasters think ?

Yes, chess masters do think "differently" than chess amateurs. You can observe their thought process when you watch a titled player stream live games, analyze, or calculate out loud.

Yes, you can gradually begin thinking like they do, but this process isn't a switch you turn on and off. You gradually reach their level of thinking only after much experience and chess study.

The reason titled players are so fast (and accurate) during bullet and blitz chess is because of something called "pattern recognition." This is something ALL chess players use, but chess masters have been exposed to many more chess patterns than the average player.

Here is a recent video from GM Daniel (Danya) Naroditsky and puzzle rush survival is not timed, so he explains his thought process in a teaching way:

Grandmasters don't calculate 10 steps ahead. They just move because they recognise the position and are capable of intuitively coming up with a plan spontaneously. Typically known as pattern recognition. The only way to practice this is to play regularly

Kotov wrote Think Like a Grandmaster about this.

'When my opponent’s clock is going I discuss general considerations in an internal dialogue with myself. When my own clock is going I analyse conctrete variations' - Botvinnik

I cant reckon why Fide and Uscf gives GM titles for free. They are not true GM. They use pattern recognition and memory perfect lines of dead gone champs. There are some thinking GM of course. In fact you want to think bullet chess but this is a dream to think so fast and not going wrong. Human brain can catch with some speed the signals of right or wrong or win and blunder moves but the other logic concepts that rise and hold a drawish game or a long strong battle the human brain is slow to think if and or so logic priorities

What they think I'm thinking:

What I'm really thinking: