There a few other rules for team sorting:
1) a cow cannot come back after it passed the gate
2)the rider cannot touch a cow intentionally (foot, stirrups, reins)
3)horse can push them, but are not supposed to harm them (bite cows...)
And if you want to get a faster time you will alternate gate horse/rider
For team penning:
1)you don't have to "pen" all three cows, but in the standings 3 cows are better than 2, 2 better than 1 regardless of time.
2) there is an imaginary line across the arena: you cannot have more than 1 "dirty cow" (number not called) at any given time pass the line and such cow should be sent back across the line before finishing.
3) you usually finish with 2 riders(out of 3) entering the pan with the cows
The events are a ton of fun, an I guess there are small variation across various regions and associations.
There is also another event called in-and by where you have a rectangular pen (12 feet wide) and 10 numbered cows are jammed at one end. There is a side pen (to the right usually) connected to the rectangular pen. Odds or even are called and 2 riders have to send the appropriate cows either in the side pen "in" (one rider stands by the gate) or to the other end of the rectangular pen "by". If the wrong number( odd/even) goes in the side pen or to the other end you DQ. Fastest time wins.
We have been doing all this events for a few years....I actually do them on my almost 18h Shire....and yes cows did try to go under him...