That photo is showing chicks with different alleles at the e locus:
E (Extended black)
ER (Birchen)
eWh (Wheaten)
e+ (wild type, sometimes called Duckwing)
eb (brown, sometimes called Partridge)
ebc (Buttercup, because it was found in the Buttercup breed of chicken)
Db is a different gene, at a different locus. It restricts black, similar to how the Columbian gene restricts black.
I find that photo on this page:
http://www.edelras.nl/chickengenetics/mutations1.html
And there is a note:
"Above are the typical e locus down patterns, without columbian-like restrictors (except maybe ebc chick- Db)."
So the ebc chick might have Db as well, or it might not--the person writing the page is not sure. But ebc and Db are two different genes, not different names for one gene.