Do they all have 4 pigments, or do they have up to four pigments?

They have different pigments. All the four pigments cannot be in one animal. It is the varying pigments that gives their blood different shades of colour - green, yellow, violet etc on the other hand we humans have majorly red colour conferred by haemoglobin.

Regarding the white blood cells, definitely theirs vary from that is humans though not Much. In animals, theirs is mostly called haemocytes (also function like wbc in Humans) case in point animals that have a closed circulatory system (blood system made up of a heart pumping Blood through blood vessels) like Humans but in none mammals.

In summary, animals have similar wbc as humans depending on specie and secondly the difference can easily be detected through their quantity. Wbc in animal are more abundant than in humans, just the way glucose is found more in the plasma of an animal than in humans.