As someone who currently has 15 different types of cheese in the house, and a deep appreciation of cheddar especially, I'll offer a couple comments.
If you like Tillamook cheddar, which is quite good, try to get their older ones, which they do sell from the factory but I've never seen in the supermarkets. They do have 3 & 5 year old cheddars. I usually call if I'm down on the coast of Oregon and make a point to stop by if they are selling such, which they do not always do.
You can get cheddar in France, and nice ones too. But they are usually only in the cheese shops. The large Carrefour near me in St Avold has cheddar at the counter, not in the aisles, (This means they sell it cut off a block, by weight, not prepackaged.) In Nancy I found some at a very good shop, but it was quite obvious they don't sell much of it. It really helps to speak the local lingo.
I have a 18 month old "Grand" that's quite sharp and very much like a cheddar that | got in France, along with several other cheeses from the same shopping spree. I also picked up an aged Gold in Frankfurt that's very similar and goes very well with red wine. I get English cheddars every couple months when one of my friends goes over the Channel to visit family, and there are a couple brands that are available in the store locally.
I have family in Wisconsin and used to receive care packages on a regular basis, but that's out now due to shipping issues.
What I have found is that there's more variation between manufacturers than can be laid strictly on location. There are some fairly poor American cheeses sold as cheddar. There are some extremely good cheeses that resemble cheddar sold under different names. Half the stuff in my stock doesn't have a specific "name". "Rustic" is a category that covers a lot of ground over here.
If I had to say any one thing that sets the English apart from a lot of the others is that it's not as hard when it gets older. And that's pretty broad.
And since I'm still learning to appreciate the verities offered in this part of the world I don't pay as much attention to the name as to the taste and texture.