From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
The rush attack (ラッシュ アタック, Rasshu atakku) is a generic term for a basic type of physical technique in which the user utilizes physical attacks in rapid succession against their enemy. They often appear in Dragon Ball, Dragon Ball Z, and Dragon Ball GT along with films, manga, and video games. Unlike in the case of energy waves or energy spheres, rush attacks do not require any energy, only relying on hand-to-hand combat such as martial arts and other physical fighting styles. Many fighters can perform rush attacks, and the power, strength, and speed varies upon the user. Through training, concentration, and transformations, rush attacks can be further increased.
In the Budokai Tenkaichi video game series, they serve as Blast 2 or Ultimate Blast attacks and seem to inflict more damage as Ultimate Blasts than as Blast 2 attacks. Similar to energy waves, if two characters use their respective rush attacks against each other, they will collide in an Energy Crash. If one character loses the Energy Crash with their rush attack, they will be knocked away by the winner. While this occurs in Dragon Ball Z: Budokai Tenkaichi 2 and Dragon Ball Z: Budokai Tenkaichi 3, in the first game of the series, the winner will not only knock the loser away, but will automatically attack the flying opponent with their rush attack they used in the Energy Crash.
In the Raging Blast video game series, there are some rush attacks that can be used as counterattacks. They function differently from regular rush attacks as they are activated when an enemy tries to attack the character. Precise timing is required , however, along with the fact that the character must be directly in front of the attacking opponent to activate the counter rush attack. If opponent A activates a counter rush attack from a distance away from opponent B, the attack's effect will wear off and opponent B will be able to attack the opponent A.
As stated above, rush attacks do not require energy, however, they can be accompanied with an energy wave or energy sphere at the end of their usage as seen with Son Goku's Meteor Combination. In the Budokai Tenkaichi and Raging Blast video game series, some characters are able to perform this kind of rush attack, though the color of the energy attack varies with the user.