Observations inSeek are not synced between devices, they are only stored within the app itself. The iNaturalist link is there only for submitting an observation to iNaturalist, it’s a one-way connection. So this is why the counts are different between your devices. We tried to make this more clear in recent version of the app, since it definitely wasn’t clear before. But this screen only appears when you log in to iNat via Seek:
We are looking into the possibility of being able to sync data between devices, but I can’t make any promises. A major impetus for Seek’s creation was to make a privacy-first alternative to iNat which doesn’t, by default, put any personally identifying info onto our servers.