Fire pits are one step above a simple fire ring. The pit is a raised bowl made out of any number of materials. The bowl holds the fire off the ground, and most fire pits allow those gathering around it a 360-degree view of the roaring fire. Some come with a screen; screens protect by keeping flying ash and other debris inside the bowl.
Sometimes a chiminea is referred to as an outdoor fireplace. These clay (or similar material) structures have a wide bowl at the base with a mouth for feeding firewood. They also have a taller, skinny chimney to allow the smoke out.
Outdoor fireplaces are much like indoor fireplaces. You can build them out of brick, stone or any other material you would build an indoor fireplace out of. They don't allow for a 360-degree view of the fire, but do add to the "outdoor livability" of your patio.