My puzzle rating is 1604; my rapid rating is 1156. What does this indicate?
After not playing chess for 43 years, I began playing again about 3 yrs ago. My highest rapid rating, after a few months of being on chess.com was 1181, back in May. Now my rating is 1156. I just starting playing "Puzzles" about a week or so ago, and I feel it is helping me with my game. My puzzles rating is 1604. What do you think the difference between my rapid and puzzles rating indicates? Does it point to anything I need to change in my studying/playing to improve?
It means that you are a perfectly normal player.
It's usual for players to have puzzle rating of 500 above their usual favourite time controls.

After not playing chess for 43 years, I began playing again about 3 yrs ago. My highest rapid rating, after a few months of being on chess.com was 1181, back in May. Now my rating is 1156. I just starting playing "Puzzles" about a week or so ago, and I feel it is helping me with my game. My puzzles rating is 1604. What do you think the difference between my rapid and puzzles rating indicates? Does it point to anything I need to change in my studying/playing to improve?
It's easier to spot and calculate tactics when you know there is something in a position. It's a totally different story when you have to reach such positions in games and be able to spot and calculate them. Add to that opening, endgame, and positional inaccuracies or errors, time issues, and outright blunders, there's little surprise there is a difference in the ratings.

Puzzle ratings here generally seem to have no correlation other than being hundreds of points higher than ones game ratings.

Like you, I'm back at chess after an extended layoff (since 1997 in my case).
I'm doing a lot of puzzles (and resetting repeatedly when my success rate drops below 60%). My peak puzzle rating is 2509. My highest chess.com rating is for rapid and that went through 1300 for the first time this week.
I'd say you should do some more puzzles!
After not playing chess for 43 years, I began playing again about 3 yrs ago. My highest rapid rating, after a few months of being on chess.com was 1181, back in May. Now my rating is 1156. I just starting playing "Puzzles" about a week or so ago, and I feel it is helping me with my game. My puzzles rating is 1604. What do you think the difference between my rapid and puzzles rating indicates? Does it point to anything I need to change in my studying/playing to improve?