Watching recaps of the 2021 Candidates Tournaments, so many games end in consecutive repeating moves. I have a general impression that lots of top level games are drawn by repeating moves. Why do the grandmasters do this instead of offering a draw?
A repetition giving the opponent the opportunity to claim a draw is a de facto draw offer but not a de jure draw offer.
What does that mean? Well the "de facto" part means that in practice it has the same effect as a formal draw offer while the "de jure" part means that legally it is not a formal draw offer.
Psychologically it makes a subtle difference but practically it makes an important difference. The difference is the legal aspect. Why is this important?
According to article 11.5 of the FIDE Laws of Chess:
11.5 It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area.
Normally arbiters interpret this to mean repeated draw offers in a small number of moves. That is why you are instructed to notate your game as follows in Appendix C.12 -
C.12 The offer of a draw shall be marked as (=).
Repeating the position does not constitute a formal draw offer and so cannot be part of a claim of disturbance due to repeated draw offers.
What do you think the psychological difference is?
When you ask for a draw you are a supplicant. It's like you are asking for a favour. "Will you please give me a draw?"
When you repeat the position you are saying something completely different which is why in some positions the experts advise you to repeat once (so no possible draw offer) to demonstrate dominance, let the other player know who is the boss.
If you are a much lower rated player and you repeat twice in a forcing situation you are effectively saying "What ya gone do, punk? Repeat and give me the draw? Or deviate, play a bad move and give me a chance to win?"
I have won several games with that exact tactic. It's surprising when it works but some players have more ego than common sense. It's like their response is something like "No way am I accepting a draw against you. I'm so much better than you that I can beat you from a losing position". I have to admit I've been on the opposite side too. I've played a bad move rather than accept the draw and I've paid the price.
In many top level tournaments you are not allowed to offer a draw before a certain number of moves are played (often 30 or 40). The purpose of such a rule is to prevent very quick draws.
However, one of the ways to make a draw anyway is to simply repeat moves.
Even if that rule is either not active or the move number has passed, it may still be encouraged to do, if nothing else to have the game end naturally for the spectators, rather than by agreement.
Often, Grandmasters need to reach the 40-move mark. This standard time controls gives them 30 extra minutes if this milestone is reached. Often times, they will play very similar moves just to get pushed past this time, and may end up drawing here as well
In the endgame, grandmasters seldom offer draws. So may games end in draws, but they will always try to play them out. Offering a draw is not as concrete as playing a draw, where there is still a chance to continue it out.
While the existing answers are great, and relevant to especially OTB tournaments, it's worth noting in online matches there are often extremely short time controls with players moving (or even pre-moving) so quickly, it's only possible to obtain a draw by repetition. The act of offering a draw and waiting for the opponent to accept or decline would simply take far too long.
A recent example of a draw offer ending badly would be the GM Eric Hansen vs GM Hikaru Nakamura match, described here on Reddit. Also see the video for yourself if you wish to make your own mind up what happened.
Quote from the Reddit post linked above
Eric and Hikaru are playing a blitz match, Hikaru is winning 2-1.
They reach an endgame that is better for Eric, although theoretically a draw. Hikaru has around 10 seconds, Eric 5.
Hikaru doesn't offer a draw, instead tries to flag Eric. Eric doesn't go down easy though, and almost neutralizes Hikaru's time advantage. Eric offers a draw, which Hikaru doesn't respond to and keeps playing. Eventually Hikaru loses his time advantage completely, and they both have 4 seconds each.
Hikaru offers a draw which Eric didn't notice since he assumed Hikaru was trying to flag him. Hikaru simply lets his clock run down to 0 and accuses Eric of intentionally trying to flag Hikaru to gain rating.
Hikaru leaves and starts playing Alireza instead, calling Eric a liar and saying that he has bad etiquette, which is SUPER ironic since Hikaru is the one who flags his opponents in the most dead drawn positions.