In the matched grip each hand holds its stick in the same way. Almost all commonly used matched grips are overhand grips. Specific forms of the grip are French grip, German grip, and American grip.
The matched grip is performed by gripping the drum sticks with one's index finger and middle finger curling around the bottom of the stick and the thumb on the top. This allows the stick to move freely and bounce after striking a percussion instrument.
In French grip, the palms of the hands face directly toward each other and the stick is moved primarily with the fingers rather than the wrist as in German grip. This allows a greater degree of finesse, which is why many timpanist prefer French grip. Because this grip uses the smaller and faster finger muscles, this grip is used by single-stroke champions. It also comes in handy for playing fast tempo swing or jazz for the ride cymbal. For louder strokes, the wrist rotates much in the same way as when hammering a nail.
In German grip, the palms of the hands are parallel to the drumhead or other playing surface, and the stick is moved primarily with the wrist. German grip provides a large amount of power, but sacrifices the finesse provided by the use of the fingers as in French grip. It is used when power is the primary concern, such as when playing a bass drum. This is also the primary grip for the Moeller method.
American grip is a hybrid of the French grip and German grip. The palms of the hands typically are at about a 45-degree angle, and both the fingers and wrist are used to propel the stick. This grip is considered a general-purpose grip by percussionists because it combines the power of German grip with the finesse of French grip.
Traditional grip (also known as Orthodox grip). Unlike matched grip each hand holds the stick differently. Commonly, the right hand uses an overhand grip and the left hand uses an underhand grip. Traditional grip is almost exclusively used to play the snaredrum, especially the marching snare drum, and often the drum kit.
This grip is called traditional because it descends from the past when the snare drum was carried over the right shoulder on a sling. Since the drum is tilted, using an overhand grip on the high (left) side of the drum forces the elbow in a very awkward position. In this case, an underhand grip is much more comfortable. Even when the drum is on a stand, many drummers will tilt their drum when using traditional grip, although tilting is not required. Many drummers use traditional grip on drums that are perfectly horizontal, especially in marching percussion.
With the underhand grip, there are several different techniques employed which involve slight variations in finger positioning and usage. Hold your hand in a Karate position. The stick rests in the space between the thumb and index finger, and the two fingers close around the stick with the thumb atop the index at the first knuckle. The middle finger then rests slightly on top side of the stick (typically the side fingertip is the only contact made). The stick then rests on the cuticle of the ring finger with the little finger supporting the ring finger from below.