Cheddar cheese is a relatively hard, off-white (or orange if spices such as annatto are added), sometimes sharp-tasting, natural cheese.
Then further down it says:
"Cheddar made in the classical way tends to have a sharp, pungent flavour, often slightly earthy. The "sharpness" of cheddar is associated with the levels of bitter peptides in the cheese."
(by classical way, they mean aged in the caves in Cheddar)
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Its really confusing, but "mature" which they consider "sharp" is not the same as our "sharp" technically... a true sharp is above mature cheddar in sharpness, look, m not slagging off English varieties of cheddar, but for the most part, they do not recognize sharp cheddar as a separate sub genre , its just kind of thrown in with cheddar, whilst we Americans do.
Americans do not have the mature varieties that they have here, but kinda blew right past it and went right to sharp varieties. its like pickles here , everything is a gherkin, whilst Americans have WAY more categories of pickles, and gherkin is just a sub variety.