If you buy your black pepper already ground, be aware that it may contain papaya seeds. This is a cheap mix-in, as ground papaya seeds look and taste almost exactly like black peppercorns.
Fresh black peppercorns should break into large pieces when crushed. There shouldn’t be much of a fatty trace there if the product is of a good quality. If it is not, the peppercorns would become very dry when crushed. If you’ve bought old peppercorns, they would split into small pieces when you grind them.
White pepper should be creamy and slightly coffee colored. If it is too white it will likely be bleached.White peppercorns also don’t have shells, unlike their black counterparts.