Here are the the differences between the many types of mutes you can use on your instrument. During my younger years and when I played professionally, I used mutes a lot, and you should always have a mute or two in your instrument case.

There are two basic types of mutes:

1. Orchestral mutes: These kinds of mutes do not make your sound much quieter, but they change the quality of your sound. There are rubber and metal ones, and each mute changes your sound a little bit differently. These mutes can be used in a variety of situations. They are usually used in chamber music, orchestral playing and solo playing. They dampen your sound, but you will still be audible to people in other rooms or down the hall if you play loud enough.
2. Practice mutes: The primary reason for a practice mute is to greatly dampen your sound, so pretty much only you can hear you play. These mutes are especially helpful if you find yourself in the position where you need to practice, but you do not want to bother anybody else. Such circumstance may include: in your hotel room, somewhere in your house, your dorm room, etc. I’ve even used these mutes while on tour, like on the train on a long trip so I could practice without bothering fellow passengers.

Some helpful tips about using a mute.

1. If your mute is NOT a practice mute, you can keep it on your instrument, so it’s easy to use when you need it, and you do not lose it.
2. Keep it as far away from the bridge as possible when you’re not using it. You don’t want it moving around the instrument while you're playing because it could make noise and interrupt your sound while you’re playing.
3. Don’t use a mute too much. It dampens your sound, so it will teach you to not learn a certain sensitivity in your sound production and you may pick up some bad habits. I suggest that anytime you use a mute for a long period of time when you are practicing, that if you can, you play your instrument without a mute before putting your instrument away because it will readjust how you listen and put your mind back to a normal state.

Hope this helps!