And while the ignition cam may or may not be near the alternator or generator, it has nothing to do with it functionally.
Also, I forgot that some old Harleys have the points in a housing sticking up above the crankcase. It's debatable if this should be called a distributor though, since the spark plug wires don't go anywhere near it.
This setup is even used on modern-ish vehicles, where two transistors drive two coils to run four cylinders.
Unless your car is very old, chances are that you have a more reliable reluctor-based ignition, where instead of points you have a magnetic pickup that's triggered by a toothed wheel on the distributor shaft. That pickup drives an ignitor (which may also be inside the distributor, or it might be a separate module) which generates the high current input to the ignition coil primary.
You can twist the distributor to change your base timing, plus you have the vacuum mechanism that moves the points or magnetic pickup to adjust timing according to manifold vacuum, and it probably also has sprung weights that swing out as rpm increases, which moves the cam or reluctor wheel to advance timing.
The actual distribution part of the distributor consists of the rotor and terminals on the cap. That's what routes high voltage from the coil out to each spark plug.
On an old motorcycle, you just have the points (one set for each coil for each pair of cylinders as described above) without the distributor cap and rotor part. You can move the points around the cam to adjust base timing, and you might have springs and weights to advance timing as rpm increases. I don't think vacuum advance was nearly as common on bikes as it was on cars.
A distributor is only there to distribute the spark to the cylinders. On modern engines the distributor has been replaced by individual coils (on per cylinder).