Gi and No Gi are the 2 forms of Brazilian Jiu-Jitsu. Gi Jiu Jitsu is grappling with the use of a traditional Gi, which allows you to grab the clothing of your opponent. No Gi is grappling without the traditional uniform, instead you wear shorts and a rash guard. In no gi you cannot grab your opponent’s clothing.
To be a complete BJJ player, you should train in both. Marcelo Garcia is a good example of a BJJ player that is world class in both. He only started No Gi at brown belt, having built a strong base in Gi Jiu-Jitsu first. Usually if you start training in majority without the Gi, then you will have a much harder time adapting to the Gi. The Gi in some ways is more complex with all the grips but No Gi has many other aspects which are not found in the Gi (for ex: more brabo chokes, guillotines, footlocks than in the Gi).
Here are the main differences:
In Gi, you will of course wear a BJJ Gi. In No Gi, you wear shorts and a T-shirt or rash guard.
The Gi has a huge amounts of grips on both the jacket and pants. The most common jacket grip is the collar/sleeve grip. The grips allow you to have great control on the fight and to submit your opponent using their or your own Gi. It allows a much smaller opponent to control a bigger one. In No Gi you have more wrestling based grips such as neck, and grabbing all joints in the body. It is harder to control an opponent and can slip or power out of controls.
No Gi i BJJ is faster paced. Gi slows things down due to the natural friction of the garment.
While and Gi and No Gi are very similar, the way both styles evolve are very different. In Gi, the numerous grips and Gi material mean that alot of set ups are based on using the Gi matrerial for ex: lapel or worm guard (which is impossible in No Gi). In No Gi, you look more at taking your opponent’s back because mounting in No Gi has limited submisions, and the back position has the rear naked choke and other options. You will find No Gi players using more guillotines and brabo/darce chokes as well as using more foot locks.
It is hard to say what is more technical as both styles are different and you also have much smaller No Gi players that submit bigger ones (taking the back is a great way of doing that).
Most No Gi tournaments have slightly different rules from Gi. IBJJF rules do not allow heel hooks for Gi and ADCC (biggest No Gi tournament) allows them.
In this video Stephen Kesting explains the main diffrence and similarities between both styles of Jiu-Jitsu: