‘Well-done’ meat is obviously cooked a lot. ‘Medium’ is less cooked. These words make sense. ‘Rare’? That doesn’t make sense; so I looked it up.
Note the last sentence, which I have emphasized. If ‘rare’ is or was regarded as an Americanism, what word do/did people use instead? (Please don’t say it’s ‘blue’. That’s different from ‘rare’ in my opinion.)