Yea, just saying the gap might be bigger for someone who've focused a lot on those type of problems over playing.
Speaking of chess puzzles - I love retrograde problems (though I don't think they're beneficial for improving your play as they're more puzzles using chess rules as the 'framework').
For those unfamiliar with those - instead of finding the best move or planning ahead, you have to puzzle out what has happened in the past. Typical problems would be "What was the last (x number of) move(s)", "On which square was the queen captured", "Is castling still legal" etc.
Common to all problems is that the moves leading up to the position must have been legal chess moves - not necessarily good or rational ones though.
The book Chess Mysteries of Sherlock Holmes by Smullyan is a very good one that starts off teaching retrograde puzzles before moving on to some pretty tough ones. Absolutely recommended for puzzle fans - though it may or may not be to the liking of those just "in it for the chess".
An example:
White has just moved - what was the move?