Oxbow stirrups: Narrow stirrups sometimes made of metal and sometimes preferred by bronc riders.
It is designed to promote the release of a caught boot in a drag. Also, the bottom has a five-degree camber, making the desired heels-down position more natural.
Bell stirrups: Wide stirrups common to the buckaroo country. Wide stirrups make it easier to "trot out" for a number of miles in the big country. A long trot is the gait of choice for buckaroos that need to travel long distances horseback to reach the place where they will start to work.
I am kinda persnickety about the stirrups that I use. I will only use 3 inch roper type stirrups. Oxbows may have been designed to come off if you are getting drug, but I have yet to see someone actually make an escape from one of them. Bell stirrups have the same problem, if you fall, you can't twist your foot free to get away. I also avoid anything made of aluminum. They should be strong enough to withstand anything but I have seen people get fallen on and have the aluminum bend around their foot, essentially trapping them in the saddle.