"The saddle shoe is a low-heeled casual Oxford shoe, characterized by a plain toe and distinctive, saddle-shaped decorative panel placed mid foot."
Definitely blucher saddles as well though Oxford/balmorals may be more common/traditional.
I may be mistaken, but I was under the impression that the balmoral is defined by its construction. While saddle shoes and balmorals both have lacing underneath the eyestays,the vamp on balmorals runs underneath the lacing whereas saddle shoes have their middle piece sewn onto the vamp or have the saddle section visibly separated by stitching. Thus, with saddle shoes, the saddle section is always on top of the rear quarter and the front vamp, creating a different stylistic relationship to the quarter and the vamp than the balmoral, which is always part of or underneath the front vamp.
Obviously, I could be completely wrong on this, but I'm certain that I've heard from reasonable minds elsewhere that this is the truth? And BTW, what's Styleforum without a nice Sunday-morning debate??