Maura did a pretty good job explaining.
The three most common tables I see are...
Table II Section 2(b)- aka "timed first jump off". This is probably the most common. You go and do your first round, if you're clean you stop and wait for the buzzer. When you hear the signal you do your jump off.
Table II Section 2(c)- what Maura (and most people) refer to as "power and speed". You do your first round and if you are clear IMMEDIATELY (without pausing) continue on to your jump off.
Table II Section 1- "time first round". There is no jump off. Whoever's fastest with the least number of faults wins.
Often at our schooling shows 1 class will be 2(b) and the 2nd will be 2(c). At most rated shows they usually change the table every day. So the first day's classes will be 2(b), 2nd day will be 2(c), etc. I've been to a few shows where they've done "blue ribbon classes" (not sure what table that is) where basically if you go clear you get a blue ribbon. And "optimum time" where they give you a certain number of minutes/seconds it should take you to finish the course. They hide the timer while you do your course and you get faults for the typical things, but also for however many seconds you are under OR over the time! That's a really tricky table b/c the "optimum time" isn't necessarily the fastest time. There's another table for "gambler's choice" where they give certain jumps a certain number of points. You go and make up your own course and try to get as many jumps in as you can under a specific allotted time. I think Puissance classes are Table II Section 6... the list goes on and on! Look up the chapter in the USEF rulebook on Jumpers. It's pretty interesting!