What's the difference between gi and no-gi Brazilian Jiujitsu?
In Brazilian jiu-jitsu with a gi you wear the funny Asian pajamas. In no-gi Brazilian jiu-jitsu you wear shorts and usually a t-shirt or rash-guard top. You can grab onto the funny pajamas but you can't grab onto any clothes in no-gi.
The gi absorbs sweat, adds friction, and provides a wide variety of grips to choke, throw, and control from. Often the rules in no-gi are more permissive, particularly with regards to leg locks. Brazilian jiu-jitsu with the gi has more carry-over from judo. Without the gi there is more carry-over from modern and Catch wrestling. Wearing the gi is more traditional. Playing without the gi has more applicability to mixed martial arts.
Both are applicable to self-defense. Both are valid jiu-jitsu.