Among chess.com players who have played 10+ blitz games and 10+ puzzles, the average difference between their blitz rating and puzzle rating is 45 (blitz rating higher). The standard deviation of the difference is 374.

Among players who have played 100+ games/100+ puzzles, the difference is -205: puzzle rating substantially higher, standard deviation 320.

I'm not sure that it's ideal for ratings to be identical across the domains, but they should correlate to some degree.