This is a chart showing many different kinds of stirrups used through the years..both for men and women.
..and this is the best stirrup to use if you are riding aside. It is a breakaway stirrup designed to do just what it is named for in case of a fall.
This is another safety stirrup called a Peacock. The rubber band should pull open in case of a fall with this design, but I do know of one instance that this did not happen. Thankfully the rider was not injured!
...and as beautiful as this antique sidesaddle stirrup is, it would be the most dangerous one to use.