Correlation between rapid/blitz rating and puzzle rating

There are plenty of reasons behind why you have more puzzle rating than your rapid-game rating that are discussed below.

“Best Move” in Puzzle
In chess puzzles, there are always some strategized moves on the board, and the player is asked to play a few sets of moves to achieve success. Whereas in a live chess game, you make your own strategized structure from scratch. In short, the main reason behind which a player has a higher rating in chess live games as compared to puzzles is that there is certainly the best move exists in that position that gives the opponent the advantage of having the confidence as they only try to find out that specific best move. In this way, a player will only polish the tactical skills to find out effective moves and ignore other strategical skills that can only help the player in live chess games.

Time Availability
Another reason why chess most players have higher puzzle ratings is that they have plenty of time to apply tactics and find the best move available on the board whereas, in rapid games, players have a proper set of time to make their moves and are bound to think and strategize all plans within a defined timeframe. Experienced players play rapid and blitz without worrying about making quick strategies during a game because they are confident in strategic skills, the first strategy kit helps you polish your strategic skills so that you can play rapid games without extra pressure and dominate in your live chess games.

The Thought Process
Every chess mode has its unique purpose where a player has to think with a different set of mind. According to a study, in chess puzzles, your overall strength is represented whereas in rapid chess games a complete journey is defined from the beginning to the middle game, and then comes the end game. If chess puzzles are played regularly, a player can eventually increase more points as it discovers tactical piece structure from pattern recognition. Depending on how good your thought process is, if the patterns are identified and conquered correctly, the ratings will increase consequently.

Puzzles vs Rapid Games aggregate
Rapid games as compared to puzzles are played less frequently because puzzles are shorter. Therefore, most players like to play puzzles before any rapid games to warm up their tactical skills before their big matches. The puzzle level increases each time which affects the rating mostly in a positive way if you are consistent, hence, resulting in a higher rating in puzzles over rapid games.

It is concluded that puzzles play a vital role to polish your tactical skills in a way to find the best moves mostly in the middle game and sometimes in spotting opponents' traps. However, in rapid games, you should be tactical and thoughtful to create strategies from the start to the end game.
Your first strategy kit. Will help you get better in rapid games to manage strategies throughout the game.

Course: Everyone's First Strategy Kit
Website: Chess boost