"That horse is pretty near in that area while the other one is absolutely off."
This has nothing to do of how far or close they are, it's stating that their left side is on their near-side with the off-side being on their right side, and we always tack up the horses on their near-side, mount on their near-side, and lead them on their near-side since that was how it was done during the time when horses were in battle to make sure the swords don't poke them by the riders.
The right side of the horse can also be called far-side.
