Peppercorns are Berries from the pepper plant Piper nigrum. They can be picked Green which since they are highly perishable are pretty much only found in Asia and are very pungent, floral and hot. Green are also available Pickled and Dried. If Green peppercorns are harvested and dried you get Black Pepper.
Freshly ground Black Pepper in larger quantities, I have found 1T per Cup of Rub, is an up front, all over the mouth hot sharp bite, but fades fast. This is because the heat in Black Pepper comes from a chemical Alkaloid called Piperine. Since it is somewhat soluble in water it is easily washed away as compared to the fatty-acid of Capsaicin that is hydrophobic, repels water, and burns for a longer time. Lesser amounts of Black pepper add the flavor but no perceptible heat.
White Pepper is the internal seed of the berry from Fully Ripened Peppercorns that the outer fruit is removed. It is less hot and not as intensely floral as Black Pepper. White Pepper loses it's flavor very quickly once ground and gets bitter with age, it is best freshly ground. It should be noted that cheap White Pepper is just the seed of Black Peppercorns. Since Black Pepper comes from unripe fruit, faster to market, the White Pepper flavor is ok but underdeveloped, somewhat bland really. Quality White Pepper, from India and Vietnam found online, Asian Markets and high quality spice shops, is the seed from Ripe Berries and has a better more intense floral flavor quite different from Black Pepper.
Pink Peppercorns are an unrelated Berry, Schinus molle, although are similar looking to other Peppercorns have a completely different flavor and very little heat. They are tasty in Cream sauces.
Sichuan Pepper, from the genus Zanthoxylum there are some 250 varieties, comes from 2 plants that grow in China and are unrelated to all the above. Sichuan Pepper is the dried hull of the fruit after the fruit ripens and pops open releasing the seeds. It flavor is bright and flowery with hints of Citrus but no heat. In fact, beyond it's flavor, a main use in Sichuan Cuisine is the peppers ability to Numb the Mouth! It actually let's the diner eat more of the super spicy Japones Chiles frequently used in Sichuan cooking.
I hope this info helps...JJ