what is the space shuttle's SRB motor/engine? I do not know how the thrust in the space shuttle's SRB goes out/burns. research shows that it either an engine or motor though I'm not sure.
Whether the SRBs are called a motor or an engine is a kerfuffle, a pointless argument over terminology. One could equally well call them thrusters, which is a term I prefer. The working principles of a solid rocket motor, a liquid rocket engine, an ion thruster, a cold gas thruster, and even the hypothetical matter-antimatter photon thruster are one and the same. They all generate thrust by expelling momentum from the vehicle in a more or less collimated direction, thereby making the vehicle accelerate in the opposite direction due to conservation of momentum.
A common feature of rocket motors, engines, and thrusters is that the material that will eventually be expelled is carried with the vehicle until it is expelled. This makes these devices subject to the ideal rocket equation. In contrast, a solar sail is not subject to the tyranny of the rocket equation because a solar sail does not carry the material used to make the vehicle accelerate.
If you are asking how solid rocket motors work, they burn at a flame front, the interface between the solid propellant and the gas that is created by the burning propellant. The exhaust gas leaves the rocket through the nozzle. The flow is subsonic prior to the throat of the nozzle and supersonic after the throat. This concept of a convergent-divergent nozzle is also used with liquid rocket engines and cold gas thrusters. Ion thrusters use a shaped electric or magnetic field to produce a behavior similar to that produced by a convergent-divergent nozzle with physical walls.