Bolt names tell you the outer diameter, and the thread count. for example a 1/4-20 bolt has (roughly) a 0.25" diameter, and 20 threads per inch. On this team we use #10-32 for most common applications, and some 1/4-20 for larger things.

Bolts are used to fasten stuff together, they generally either have a nut on the end, or go into a pre-threaded hole made with a tap. They do not make threads on their own.

The three main types of bolt heads for what we do are button, socket, and flat/countersunk.

Nut names usually match bolt names, but the first number tells you the inner diameter of the nut.

Nuts go on the end of bolts to hold them in place. 

Some nuts are "lock nuts", this means that they wont come loose from vibration. lock nuts will usually either have a spiky metal ring on the bottom, or a white/blue nylon ring inside of them.

Rivets can be used to join two flat surfaces. unlike bolts, they are semi-permanent, and once installed you have to drill them out to remove them.

With rivets you care about their diameter, and what thickness of materials they can grip. For a #10 hole, 3/16 rivets are good.

The main advantage of rivets is you don't need to put a bolt on the other end, so in a situation where you can't access the back to put on a bolt, think about rivets