There are two main categories that stage lights fall into. Floodlights illuminate a wide area, and spotlights shine light on a smaller, more specific area.
These lights are usually used to flood the stage from above because they have the least amount of focus. They are also the cheapest lights because they do not have any lenses.
These are floodlights that are housed in a can-shaped container that is attached to a pivot. This allows them to be moved around when needed, which makes them suited for pairing with effects such as smoke machines.
These lights are a type of spotlights. They offer a narrow focused area of soft light that can be used to properly light an actor or an object on stage.
These spotlights have a much brighter and harder light. They are what is most commonly thought of as spotlights, and are used to draw the most attention to whatever they light.