well im not really sure what answer you are looking for. the only difference is that they are different colous. i think they all have cheek patches (lol a bit random but i usedto think sodapop was the only one who had them). the colour of them depends on the mutation of the budgie. normal is blue or purplish. to be honest they all look blue to me but ive read things that say they are purple so whatever. and then i believe the white ones are mostly all yellow budgies that have them.
one of my budgies has one cheek patch on one side none on the other
well that would be different! are you sure it doesn't have a violet cheek patch on one side and a white cheek patch on the other side of a white face? the cheek patch feathers are different to the surrounding ones so should be visible with a close look...
can you post a picture so we can see?
i love the picture of the budgies landing on the hand!!!