Haha good grief, I surrender.....it's all too confusing! I've been around horses for years.....and I am really surprised by all the different names, terms, and descriptions of all the colors and color possibilities!
The differences between brown and bay are easy to spot once you know what to look for
Let's look at this guy. He is fairly textbook for brown, making it very easy to see what you are looking at.
Brown and bay are mutations of the same gene, so they act in a similar way. Bay (A) restricts black production over the majority of the body, only allowing it to be on the "hard" points of the horse - the extremities such as mane, tail, legs, ears etc. Brown (At), on the other hand, only really restricts black production from the "soft" parts of the horse - flank, muzzle, behind the eye, elbow, under the tail etc. Brown will often allow extensive black on the rest of the horse, as we see in our test case here. Other times, however, brown will mimic closely to bay, and you can be hard pressed to see the difference. That is where winter pictures come in - brown horses tend to change from season to season a bit more than bay horses do, and it is often in winter coat that we can see the clear restriction of black in the soft parts.
Attached is an image that has the soft parts highlighted, to really bring your eye to them.