This term probably derives from a phrase coined by Shakespeare, who wrote “a horse of that color”, meaning “the same matter” rather than a different one. By the mid-1800s the term was used to point out difference rather than likeness.
'Horse of another color' is the opposite expression from Shakespeare's 'a horse of that color' in the Twelfth Night Act 2 Scene 3 where Maria told Sir Toby Belch that her purpose was indeed a horse of that color which meant that Sir Toby Belch got the same idea as hers. So, 'horse of another color' is an idea different from the other.
