Control can be either direct (eg. a limb) or proxy (eg. the gi).
There are two ways to control your opponent: directly or by proxy. The availability of these options will depend on the attire of your opponent. Each of these have strengths and weaknesses.
Direct control means you are grabbing a portion of your opponent’s body; a wrist, ankle, or torso. These grips tend to require timing and speed, and are not as sustainable as proxy control grips. As a match plays out, these controls become increasingly more difficult and slippery due to excessive sweating. Direct control also allows you to directly access the joints in your opponent’s body, which is the mechanism behind many submissions.
In no-gi, all lever control will be direct.
Proxy control means you are grabbing something attached to your opponent, rather than grabbing their body directly. This includes the lapel, collar, sleeves, pants, and belt. Once achieved, these grips are more sustainable than direct control, and can be maintained more reliably. It can be a challenge to prevent proxy control from your opponent because there are so many grips available. For example, if you break a sleeve grip, your opponent can always switch to the other sleeve, the collar, or the pant leg.
Proxy control can also be either loose or tight, depending on the tension of the cloth. Tight control makes it easier to pull your opponent off-balance and apply submissions, but it may also allow your opponent to break the grip or exert control against you. A looser grip is sometimes desirable because it’s much harder to break. Understanding the gripping tension, sequences, and possibilities of proxy control is the primary difference between gi and no-gi grappling.
Obviously, proxy control applies exclusively to the gi.