I believe the woodpeckers on page 2 are both great spotteds - the left being a female and the right one being a juvenile, hence the slightly different plumage - they have a red crown and are more dappled when young. Lesser spotteds don't have red bottoms, though they do have the red crown.
The male great spotted has a red flash on the back of its neck, which can't be seen from this angle, but the female is perhaps more likely to bring young to a feeder. We have a lovely lady who comes into our garden every day and always brings her young each year when she has them. I'll see if I can find some photos. I am a keen amateur photographer and very interested in the natural world.