There are many types of persimmons but they are broken into two categories: astringent persimmons (like Hachiya), which are inedible when firm and need to become very soft and ripe before they can be eaten, and non-astringent persimmons (like Fuyu), which can be eaten hard, like an apple, or soft. Fuyu are short and squat, like a tomato, while Hachiya are pointy like an acorn. More information here.