All you colour experts..

All 3 are the same.
The 'proper' term is brown, but it largely get's called dark bay over here.

Browns are black based horses, which means they have at least one copy of the extension (E) gene. 'E' is dominant over 'e', so they are either E/e or E/E. If they are e/e, they are chestnut.
At the agouti allele (controls the distribution of black pigment), they have at least one copy of 'At', the other being either another 'At' or 'a' (black/no agouti). They cannot have 'A' (bay), as that is dominant over 'A+', 'At' & 'a'.

The phenotype is the 'soft'* parts have red hair, the rest black, but some can be so dark they pass for black.

*muzzle, 'eyebrows', flanks, girth, base of ears

Interesting links:
http://www.horse-genetics.com/brown-horses.html
http://www.equinegenetics.blogspot.com/
 
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