These styles of cheese use production methods that remove more moisture from the cheese than any other style. Lower water activity reduces the risk of undesirable bacteria whereby preserving the milk and providing long shelf life.
Semi hard cheeses are often semi-cooked and pressed to remove excess whey. Examples include cheddar such the clothbound classics from Quickes or Montgomery’s, aged stretched curd (pasta filata) cheeses such as provolone and large mountain cheeses such as Comte from the caves of Marcel Petite.
Hard cheeses have even lower moisture, as the curds are cut to rice-sized pieces and are often reheated to remove more whey. The addition of salt and long-aging results in a very hard texture that can be smooth or granular. Long-aged Gouda from L’Amuse and Cravero Parmigiano Reggiano are superb examples.