Okay, I might be wrong but I classify demons differently.
I think that the yellow eye means fallen angel or an angel who was tortured in hell and became a demon. As we never see Lucifer’s eyes change it’s more likely the second option.
Demons with white eyes are the ones who were created. They were never humans like other regular demons. There are two of them on the show. Lilith is the first made by Lucifer, Alastair is the second who was the main torturer and almost as old as Lilith.
Demons with black eyes were humans once but their soul became twisted and black.
Now the most mysterious of the four to me are the crossroads demons. It seems like they form a completely separated cast within the hierarchy of hell. After all one of them could even become the King of the underworld. Their special position and eye color may have a connection. (My theory that both of it has somehing to do with the souls they manage to obtain. They aren’t simply plain evil but they make others fall to perdition too.)
This is usually how I think about it, but I might be wrong. Ideas?