You are mixing VARIETY (colour/colour pattern, aka APPEARANCE) names with the names of GENES. The nomenclature for genes is pretty standard worldwide. The name for varieties can differ significantly.
Brown red is a variety and is birchen based plus gold: E^R/E^R s+/s+
E^R based birds are...
The alleles of the E gene have the following dominance: E > E^R > e^Wh > e+ > e^b However, add in sufficient melanizers and e^wh becomes the most recessive. Generally extended black, birchen and wheaten are thought of as dominant with wildtype and brown thought of as recessive. BUT, it really...