I missed this question.
What is the difference between your corned beef and ours?
In the UK, or at the very least in England, corned beef is universally understood to be chopped or minced salt beef (corned beef to you), usually supplied in an oddly shaped can, bigger at one end than the other (to make it easier for the meat to slide out), and opened with a key.
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This is largely down to history. Something very similar (if not the same - I am not sure) was known during the war as bully beef, and was part of rations both for the troops and folk at home. During the 50s and 60s we imported ship-loads of the stuff from argentina. It was a cheap sandwich meat, or might be had cold with a salad, or cooked with potatoes and veg as a hash. Corned beef fritters (sliced, dipped in batter, and fried) was also a thing.
It was so much a thing, that when proper corned beef became more common on the market, we started calling what you call corned beef "salt beef".
And that is how it has stayed. I think most people who think about it, these days, aren't confused, but the names persist.
Also, nowadays, you will often see sliced corned beef in a deli, just laid out like ham, and turkey and other meats; also prepacked sliced in supermarket chill cabinets. I know for a fact that some of it comes in large commercial cans, and the butcher takes it out and slices it. But I know at least one deli who make it themselves, to a fairly luxurious standard (like a salt beef terrine).
Having said all that, I remember being served proper Corned Beef in Ireland, and I suspect that it is also called that in Northern Ireland.
1960s TV ad for Fray Bentos Corned Beef:
https://www.hatads.org.uk/catalogue/record/5c28fa53-cc8b-4308-8769-0296a94f1a5a