The number of puzzles correct is the overall score for their puzzle history. If they stayed at like 1000 puzzle rating for a long time and keep solving puzzles correctly, then their puzzles correct would be high. Pass rate refers to a specific puzzle or a rating range of puzzles. These are different things.
I may be wrong. Please correct me if I am. Hope this helps!
Chess.com puzzles are rated so that they have a 50% average pass rate. At really high ratings however, many puzzles have lower pass rates because there aren't enough people with very high puzzle ratings. So they have a lower pass rate and use a more complicated estimation to get the rating.
There are also some weird cases where a midrange puzzle has 100,000+ attempts but still hasn't settled at a ~50% pass rate - I don't know what's going on with those.
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I have solved some high rated chess puzzles, so I know that the pass rate tends to vary from 1% to 53%. The average pass rate of a puzzle might be something like 25%.
But when I check people's puzzle stats, they have about 50% correct.
How does this add up? I know that the pass rate can be quite high for low rated puzzles, but I'm talking about puzzles rated from 2000 to 3000, and people who solve puzzles in that area.