The short answer to this is: one is practiced in the gi (jiu jitsu kimono), and the other is not. Duh. But that's a gross oversimplification. While gi and no-gi jiu jitsu are inherently the same, there are subtle differences in how they are practiced.
Want to delve into the nitty-gritty differences between these two sides of Brazilian Jiu Jitsu? Read on...
As noted earlier, the most obvious difference between gi and no-gi is the attire. In gi jiu jitsu, practitioners wear a gi, while in nogi jiu jitsu, practitioners typically wear snug-fitting athletic apparel. A Brazilian jiu jitsu gi consists of a jacket, usually made of 100% cotton, a pair of pants - made from either cotton or a poly-cotton ripstop - with a drawstring closure, and a belt that is tied around the waist over the jacket. Male practitioners can opt to go bare-chested or wear a rash guard under the jacket. Female practitioners opt to wear either a sports bra only, or a sports bra and rash guard. In no-gi jiu jitsu, both male and female practitioners usually wear a rash guard paired with grappling shorts - or compression shorts, no pockets - spats, or both shorts and spats.
Another obvious difference is in the grips. In no-gi, you don't have the material of the gi to grab and use against your opponent, and you are not allowed to grab and use the material of the rash guard and shorts. This leads many in the gi community to make the - inaccurate - remark, "there are not grips in no-gi." In fact, there are grips, they are just modified. Instead of grabbing the lapel, sleeves and pants, practitioners in no-gi use a lot of monkey and c-grips, grabbing the wrist, back of the neck, back of the ankle, and bend of the elbow. Gable grips are also used to their best advantage in no-gi.
One of the biggest deterrents for gi practitioners to practice no-gi is the belief that no-gi jiu jitsu requires more athleticism. Yes, the more successful competitive no-gi practitioners typically tend to be more athletic - quicker, more explosive, and better able to scramble - just as with gi jiu jitsu, proper execution of technique can overcome a stronger, more powerful opponent. Additionally, the lack of material-based grips allows for both you and your opponent to slip out of positions a lot easier. Therefore, there tends to be a lot more movement in no-gi jiu jitsu than in gi jiu jitsu, where one can maintain a more secure grip and prevent his/her opponent from moving too much.
Of course, without the gi, you can't possibly do any of the awesome lapel chokes that you can with the gi. Additionally, a lot of the modern sport jiu jitsu guards - such as leg lasso, spider guard, worm guard, etc. - are essentially impossible. On the other hand, the lack of gi also makes a lot of techniques and submissions easier to execute. For example, wrestling takedowns are far more successful when your opponent can't grab a hold of your lapel and stiff-arm you away. Some chokes - such as the mata leao and the d'arce choke - are also easier to lock up when there isn't a lot of material around your opponent's neck impeding your movements. The lack of material also makes it easier for you to escape certain submissions, such as arm bars and triangles.
Gi tournaments - and divisions - are typically the most popular and have larger numbers of competitors. The IBJJF World Championships - fought in the gi - is widely considered the most prestigious event in the world of competitive Brazilian jiu jitsu. The Abu Dhabi Combat Club (ADCC) Championships is considered to be the most prestigious no-gi event in the world. While most tournaments, both gi and no-gi, are points-based, there is an increasing demand for submission-only tournaments. This is particularly the case - and far more successfully executed - in no-gi, where the sub-only ruleset favors more the faster, more athletic and dynamic no-gi game in which competitors have fewer opportunities to stall.
Regardless of whether you prefer gi or no-gi, it is widely believed that practicing in the gi can help your no-gi game, and practicing no-gi can help your gi game.
Train on... gi or no-gi. Oss.