I think we're talking about a standing martingale right?
A tiedown and standing martingale are capable of serving similar purposes but when the standing martingale is used, it should not be used to brace against. It should be used so the horse either a) can't hit you in the face over jumps, b) can't get their head over the point of control, and c) when hunting, it was my undrstanding it would help protect the horse in case of a fall.
I'm not hugely english experienced so someone is welcome to add as well, I only know the basic stuff from my brief endeavor.
When a tiedown is used in barrels it's intended to help the horse balance. The standing martingale shouldn't do that. So many of them are adjust incorrectly to be used similar to a tiedown.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.