Actually, the stuff generically called 'chalk' refers to several different compounds. Blackboard chalk is indeed usually calcium sulphate these days, but the rock chalk found for instance in many of British hills is calcite (calcium carbonate) and used to be used for writing. The term 'chalk' is still used even though the actual material is different, the same way that people still refer to "lead pencils" when they haven't contained lead for years.
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Actually, the stuff generically called 'chalk' refers to several different compounds. Blackboard chalk is indeed usually calcium sulphate these days, but the rock chalk found for instance in many of British hills is calcite (calcium carbonate) and used to be used for writing. The term 'chalk' is still used even though the actual material is different, the same way that people still refer to "lead pencils" when they haven't contained lead for years.