The legendary story of Darwin's Finches of the Galapagos is that the variation in the bills of the finches on different islands led Darwin to suspect that species were not immutable and that different needs based on the environment could drive the development of different species. However, as shown on the Mockingbird page, it was the variations in coloration and bill size of the Mockingbird that originally intrigued Darwin, not finches.
The Large, Medium and Small Ground Finches are distinguished by their body size and the size and form of their bill. The different beaks were evolved to handle different sized seeds and other food. The sexes are distinguished by color. If the finch is black is it is a male. If it is brown it is probably a female but could be a young male.
The bill of the Large Ground Finch Geospiza magnirostrisis large with a bulbous and upper curved lower bill. This is well shown in all of the photos.