What is White Cumin and Green Cumin?
The question is "what is language and why the people cannot stick to one original name?" ;)

What could be find under "white/sweet cumin" is actually aniseed (and sometimes it's called green cumin). What is "green cumin" is dill seeds. 

The way to go is to look for latin name or the look of it. What could be more troublesome is difference between Roman Cumin and Persian Cumin (very, very very often treated as same thing). Roman cumin is much more mild than Persian (or sometimes even called Turkish) one.  

White cumin might be regular cumin just looking "whiteish" because of the place of origin but might also be aniseed but it could be lost in translation of the recipe.