Solid Rocket motors can be classified by many different parameters. Some of these parameters, like brand, impulse, and average thrust, are often included in the motor's designation.
The most common and helpful way to classify motors is by impulse class, which is a well-known grading system that splits motors into groups based on consistent total impulse ranges. The impulse class can give rocketeers a good idea of the power of the motor. Motors are generally designated with their class (Eg. the AeroTech J350W has the J classification).
Brand is another important classification. The brand of the motor is especially important in the compatibility of the hardware set. Often one brand's hardware set is not fully compatible with another brand's motor, so special cross-loading hardware is often needed in this case.
Another important classification is the type of propellant. Generally, most brands make their own proprietary propellant, which is used for a few of their motors. Motors with the same propellants have similar motor performances, and certain propellant types might be banned from certain competitions.