There are a number of different types of orienteering. Foot orienteering is the most common but there is also mountain bike, ski, and trail orienteering. Within each type there are various types of race.

Disciplines

Foot-O:
Foot orienteering (Foot-O) is the most common type of orienteering in Canada. Competitors walk or run around the course visiting the controls in order.
Ski-O
Similar to Foot-O but on cross-country skiis. The map is a standard orienteering map with the trails higlighted to indicated navigability.
MTB-O
MTB-O is also similar to Foot-O but the competitors ride bikes and so generally have to stick to trails. The map is attached to the handlebars.
Trail-O
In Trail-O, competitors have to stay on the trails but the controls themselves are off the trail. When the competitor reaches the area of the control, they have to successfully identify the correct control from a number that will be visible.
Rogain
Rogaines are events with a time limit rather than a set course; competitors try to visit as many controls as possible within the allowed time. Each control is worth a number of points based on how difficult it is to visit. The competitor with the most points wins. Rogaines are typically longer events — with time limits of 6, 12, or even 24 hours — and use a map with less detail and participants compete in small teams.
Adventure Racing
Adventure Racing often contains stages of orienteering or requires navigation in other stages.

Types of races

Sprint
The shortest races, these feature courses with many controls and shorter legs in between. Sprints are typically raced in urban or urban park environments and use a slightly different map design.
Middle Distance
Both Middle and Long Distance races the more "traditional" orienteering races, typically taking place in larger forested areas with a moderate number of controls (fewer than in Sprint races).
Long Distance
Like a Middle Distance Race, but longer.
Relay
Teams of 2 or more competitors, running one at a time on their own course. There are a variety of relay formats. In championship relays, Unlike individual races where competitors run by themselves, all first runners start at the same time and run a variant of the same course.