Do different types pasta cook at different times (brand, shape, whole wheat)? I know there is no exact science to cooking in general but I was wondering if there is a statistical difference in the respective cooking times.
Pasta definetely does have (sometimes vastly) different cooking times. Thin noodles like angel hair spaghetti might be done in 3 min, and al dente in 2 min, while e.g. penne rigate or rigatoni often need 10min+. Whole wheat noodles also tend to need to cook longer for the same pasta type, and often don't get as soft as wheat noodles.
That being said, check the box or bag your pasta came in, it should include approximate cooking times. If you like your pasta softer, cook it for a little longer than what is recommended, if you like it al dente, cut it short. The best way to find out is to taste regularly towards the end of the cooking time.