There are probably at least as many types of potentiometers as there are resistors. Potentiometers for all types of purposes. This page dives in deeper to let you know many of the types you'll find available.
Exactly like normal, fixed resistors, potentiometers are rated for a maximum resistance measured in Ohms. Often it is in thousands of Ohms (1000 = 1K), or millions of Ohms (1,000,000 = 1000K = 1M megohm).
For reading varying analog voltage readings like in this guide, 10K to 100K Ohm potentiometers are ideal. Be aware there are many different values available from resellers.
Not all potentiometers are the same physical size. Most often the size relates to the power capacity of the potentiometer but not always.
If you are breadboarding a circuit, look for potentiometers that are breadboard friendly meaning the terminals fit a 0.1" grid of pins. Adafruit sells many breadboard friendly potentiometers.
For other uses, you will want to measure the space you have in your project or project enclosure to see if your planned potentiometers fit. Also consider ergonomics, will the potentiometer be placed to be easy for the user?
Potentiometers made to be mounted on an enclosure are called Panel Mount Potentiometers. They come with a nut to hold the potentiometer to the panel. The shaft most often makes accomodation for a knob to move the shaft.
Adafruit sells potentiometers that are both breadboard friendly for prototyping and panel mountable for making a finished project easily. The best of both worlds for Makers.
The most common potentiometers have a knob or shaft of some sort and and you twist the knob to change the value.
Sliders, straight running potentiometers, move along a rectangular track to move only up and down. They are often used for audio mixing and lighting control.
Getting more exotic. Most potentiometers for regular use are linear taper potentiometers. The value of the resistance varies linearly as you adjust it, from 0 to 100% of the adjustment. In the examples in this guide, this gives a nice, even set of numbers and pixels as the potentiometer is adjusted.
In some circuits/projects, a different type of resistance is better. For example, the human ear doesn't perceive sound linearly but rather logarithmically. So some audio applications and other circuits use potentiometers that vary the resistance logarithmically to mechanically vary the resistance to a log scale. They still give 0 to 100% of the value, just not in a "twist 10 degrees = x" amount of resistance through the whole adjustment range.
Adafruit sells potentiometers with analog and logarithmic tapers - when you are browsing the catalog, be aware of this distinction.
You want to ensure you use the correct type of potentiometer for your application. If you are unsure, go with linear and you can substitute later.
Some applications, such as audio, benefit from adjusting two potentiometers via one shaft. Those are called dual potentiometers. More rarely there could be three or more stacked on one shaft. These come in linear and logarithmic tapers.
Some potentiometers come with an on/off switch mounted on the back of either a single, dual, or stacked potentiometer. This is great for using the same knob to both turn on a circuit and adjust parameters.
You may see potentiometers on circuit boards rather than on a panel for user control. These most often are usually left in one place, maybe adjusted during calibration of a circuit. These are called fixed potentiometers as they keep a fixed value unless you open things up and tweak them. They may be adjustable via finger or screwdriver.
It seems strange to fix a value of an adjustable device but it does make things handy for tweaking things on an irregular basis.
Most potentiometers adjust in a single motion from one extreme to the other (0 to 100%). There are some potentiometers, usually smaller ones inside a circuit) that can turn more than the standard amount, they can be adjusted (usually via screwdriver) over multiple turns of the wiper shaft. They provide a greater range than single turn potentiometers, providing greater accuracy. Most often they are not adjusted often, maybe during a circuit's calibration.
Like regular resistors, most potentiometers use a carbon composition to provide the resistance. The potentiometer will be rated for a certain power capacity, the voltage times the amperage it can handle, measured in Watts.
For hobby applications, low wattage potentiometers should be fine although if you are making something for sale or production, checking the wattage is necessary.
You may find potentiometers made of other types of materials: ceramic/metal (cermet), conductive plastic, or wire wound. Wire wound resistors usually are rotary and you might feel the individual wires as you turn the knob. Wire wound is most often used for high power/wattage applications or potentiometers with a small resistance.