URL 1 is using the default hidden param verifiable=true, while 2 also includes IDs on observations that are not verifiable.
26675 is smaller than 27515 because 26675 is the number of verifiable observations by tiwane, while 27515 is the number of IDs tiwane made on all of his observations. They’re not asking for the same data – the first is asking for number of observations and only includes verifiable, and the second is asking for number of IDs and includes all observations. He could (and does) have some observations that aren’t verifiable, and he could (and does) have some observations that he never added an ID to, e.g. this one. So we wouldn’t expect these numbers to be the same, either one could be larger.
The profile page includes current=true, while the identifications page shows current=any. This was a design choice that probably only the developers could comment on.