The greater Spotted Woodpecker is a medium sized Black and white bird roughly the size of a Blackbird. The underparts are a dirty white colour but the main colour indicator is that the male, female and juveniles all have a patch of easily seen red body feathers beneath the tail and a white patch on the upper wing. The male has a red spot on the back of it's head and the juveniles have a red band around the back of the neck.
The Lesser Spotted Woodpecker is a much smaller bird, again black and white but without the white wing patches. The Lesser spotted does not have any red markings beneath it's tail. The male should have a dull red crown while the crown of the female is a dirty white colour.
Hope this helps.