A "generator" and "motor" are essentially the same thing: what you call it depends on whether electricity is going into the unit or coming out of it.
A generator produces electricity. In a generator, something causes the shaft and armature to spin. An electric current is generated, as shown in the picture (lighting bolt).
Lots of things can be used to make a shaft spin - a pinwheel, a crank, a bicycle, a water wheel, a diesel engine, or even a jet engine. They're different sizes but it's the same general idea. It doesn't matter what's used to spin the shaft - the electricity that's produced is the same.
A motor uses electricity. In a motor, the electricity comes in through wires attached to the positive (+) and negative (-) terminals. The electric current causes the armature and shaft to spin. If there's just a little current and it's a small motor, it won't do very much work (i.e. it can only spin a small fan). If it's a large motor and it's using a lot of electricity, it can do a lot of work (i.e. spin a large fan very fast; lift a very heavy load; or whatever the motor is being used for).
Electric generators are essentially very large quantities of copper wire spinning around inside very large magnets, at very high speeds.
A commercial utility electric generator -- for example, a 180-megawatt generator at the Hawaiian Electric Company's Kahe power plant on Oahu -- can be quite large. It is 20 feet in diameter, 50 feet long, and weighs over 50 tons. The copper coils (called the "armature") spin at 3600 revolutions per minute. Although the principle is simple (copper wire and magnets), it's not necessarily easy!
Steam turbine generators, gas turbine generators, diesel engine generators, alternate energy systems (except photovoltaics), even nuclear power plants all operate on the same principle - magnets plus copper wire plus motion equals electric current. The electricity produced is the same, regardless of source.