Well, the differences are in the names, really. The AC generator takes a mechanical input (spinning) and outputs an AC signal. The DC motor takes a DC signal input and converts it to a mechanical output (spinning). Of course, they work in different ways, so let's go through that (see links below).
The AC generator generally works by the concept of Faraday's Law (and Lenz's Law, I suppose). You are changing the magnetic flux from a permanent magnet through a wire, inducing current in that wire. The classic example is spinning a loop of wire in a magnetic field. This causes the cross-sectional area of the wire to change, resulting in a change in the flux. The current in the wire is generated to "oppose" this flux, and is this current that powers whatever is on the generator's output.
There are many types of DC motors, however, the classic examples operate on a simple concept. You have mounted permanent magnets and a spinning electromagnet. The current is hooked to brushes that create an electrical contact to power the electromagnet. The electromagnet directs the magnetic field lines in a way that produces a "Lorentz Force," putting torque on the shaft (spinning the output). Every half-cycle, the brushes "switch" electromagnets to complete the cycle (otherwise the motor would stop dead).
So, take-away points, AC generator produces AC signal by spinning input. DC generator produces a spinning output from a DC signal.