The different types of mutes separate each other on form and material. The use of mutes makes it possible to vary the instruments sound and loudness. Further down, you will find a full description of the different types of mute and what they are used for.
Straight mutes make the instruments sound brighter and ads a nasal element to that sound. It is often used in orchestras, mainly by classical musicians and brass band musicians.
Cup mutes are often used within the jazz genre. It is basically a straight mute with a collar. The collar adds a softer and more complete sound to the instrument, then the straight mute does.
Stop mutes are an alternative to the use of the traditional hand-stopping technique. It is consistent in its sound and takes away the unhealthy pressure that the wrist has to withstand inside the bell.
Practice mutes are the tool you need if you want to practice almost silent. A practice mute is the shape as a straight mute but has closing cork or rubber around the neck to ensure that all are and sound goes inside the mute. This does produce more resistance with some practice mutes, which can affect intonation but also create a larger tone when playing without a practice mute.