A Fire Extinguisher is a small piece of equipment, essentially a small vessel, that contains a fire extinguishing agent to put out a fire. It is movable and not attached to anything.
A Fire Hydrant is a hose outlet that is either connected to the street water system, or a sprinkler system within a building.
Interesting point to note: Many people assume your typical Fire Hydrant on the side of the street is where Fire Fighters connect their hoses to and fight the fire. In actuality, the majority of the time the Fire Fighters hook their pump trucks up to the fire hydrant, increase the pressure significantly, and then discharge from the pump truck to the automatic sprinkler system within a building to increase pressure/flow through the sprinklers. This is the case for the majority of newer commercial buildings that are fully sprinkled.
Answers to a lot of other fire related questions can be found in the anthology of NFPA standards.