I believe hard cheese is the kind you buy in a block. Cheddar, Swiss, pepper jack.... It comes in an 8 oz pkg and when I buy it, I cut it into eighths and put it in a ziPlock bag. Then I can pull out a 1 oz piece when needed. Hope this answers your question.
The above comments are right. You can always do the squeeze test: if it feels about as "hard" as a block of cheddar, it's probably hard. If it's softer, like mozzarella or goat cheese, then it's a no-go!