There are just as many types of switches as there are applications for switches. They can be built for whatever need is required. To the right are some common switches.
The most basic switch, a single-pole/single-throw (SPST), is two terminals with a half-connected line representing the actuator (the part that connects the terminals together).
Switches with more than one throw, like the SPDT and SPTT below, add more landing spots for the actuator.
Switches with multiple poles, usually have multiple, alike switches with a dotted line intersecting the middle actuator.
There are also switches that look like dials and have current flowing depending on which way the dial is moved. Those are called rotary switches.
Finally, there are some niche switches for niche applications like temperature shut-offs, temporary or limit switches that act more like a button, float switches that turn on when a water level gets high enough, and more!