My Arab mare is 14.1 so I refer to her as a horse (since breed-wise, she's a horse). If the person I'm talking to doesn't know about horse heights and seems interested, I'll generally mention that she's a pony height (shorter than 14.2) but a horse breed and that, since breed takes precedence in determining horse vs pony, she's technically
a pony-sized horse.
I can't remember the specifics, but with true ponies, there's some kind of difference in body proportions. I can't remember what the exact differences are (perhaps something to do with head size vs body size??) but I know that it comes into play with miniature horses. Mini's, though technically pony-sized, have horse proportions and are therefore considered to be horses.
Well, that makes things clear as mud!