Hopefully the below clears all this up with photos and comparisions.
For the first bird checking this on a desktop it is very clear that it is not an Artic tern but the exact same Antarctic Tern that was photographed at the Mole and the one around lake Ellesmere.
You can see if you look closely at the bill all the photos show the same black dirty mark at the top of the bill near the face but there is some variation in the head moulting as photos were taken at different times, it even has the same white feather mark on the middle shoulder as the Ellesmere bird indicating that it is the same bird.
See photos below
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For the other bird its I am pretty sure it is an Artic tern that is entering breeding plumage, both photos where shot in different lighting conditions so there are factors that one looks a lot more grey than the other, I expect the Ahsley bird to get a lot more of the blood red colour on the legs and bill as it moves closer to breeding plumage.
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For the non breeding photos you can see that it compares quite well to the Artic tern that I found back in Hawkes Bay, that bird had the same leg structure as the Ashley bird, the difference in the photos was lighting where the bird I photographed looked more silver but when the light got brighter it was same grey as Ashley bird, it also had bits of red showing at the base of the bill.
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If you think that the bill is too large and doesn't suite an Artic tern remember the South American Tern that was then changed to an Artic tern with large bill by the records committee as they said there could be some variation in bill length and that bill is large for an Artic tern.
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I remember there was more Artic terns being reported 5-10 years ago and now they have dropped off and more common's being reported, it could be possible that many of the common's being reported are Artic terns in 1st year plumage.