I quickly looked at the underlying code and found that the profile number is the number of other peoples Observations you’ve added an identification on.
The identification page shows the number of Identifications you’ve added on other people’s observations.
I haven’t drilled down enough to find the cause of the discrepancy - but it’s likely to do with taxon swaps (like @cacklingkingfisher says) or perhaps something else like counting withdrawn ids on the identifications page?
EDIT:
Previous discussions:
https://forum.inaturalist.org/t/identifications-count-is-different-from-my-profile-and-when-you-click-identifications/23000
https://forum.inaturalist.org/t/what-counts-towards-a-persons-identification-counts/4165
https://forum.inaturalist.org/t/profile-identification-counts/36749
https://forum.inaturalist.org/t/3-different-stats-for-identifications-which-is-correct/47574