I'll explain that all for you.
Domination is the gametype in which there are several control points across the level. The two teams have to compete over them. You obtain them by touching them and they will turn your colour. Over five seconds, you will get a point for every control point you own. The aim is to get the maxscore before the other team by controlling more points than them.
Death CTF is Capture the Flag with a mild twist. Killing players will give you a point, and scoring a flag will give you a point for every player on the other team, and in addition to that, they will all die. However there is a flag capture delay. So basically, captures/scores and kills count.
JailBreak is the gametype in which there are two teams confined to jails at the start. They both get released into the main arena. When a player dies, he returns to the enemy team's jail. You have to run towards their jail and freeze the spring to free your team mates; of course they have to jump out of jail when you make the effort. The aim is to jail the whole of the opposing team and not get your team jailed. Can be played to a certain limit or can be timed.
Flag Run is the concept in which there is only one flag. Often in the centre of the level, you can capture the flag, and only one player will have it. That player will have to run to their base and score as fast as he or she can and making as many kills on the way as he or she can. Reaching base within 15 seconds will give 3 points, 30 seconds 2 points, 45 seconds 1 point. At 30 seconds, killing the flagholder will give you the flag. Every kill made on the way is an additional point. Max points = 6.
LRS is primarily about survival, while XLRS is about kills and survival. In LRS you just need to be the last rabbit standing, but in XLRS, your kills multiply based on what position you rank. 4th and below will multiply by 1. 3rd = x1.125, 2nd = x1.25, 1st = x1.5.
Domination, Jailbreak and Flagrun need certain levels for their gametype to work. You can find some of these on J2O and some on the JDC website under files. Death CTF works in any CTF level and LRS/XLRS works in any level, but is supposed to be played in battles only =P.
For more information I would reccomend checking
www.jazz2online.com/jdc and looking under event descriptions.
Hope it helped.
~Rag
Edit : NOW I WASTED MY TIME. I didn't see a post above mine )=