What what you describe, probably running a carburetor? So no fuel injection or computer to control the timing advance.
99% of the time you want vacuum advance (which comes with mechanical advance as well) The mechanical advance comes into play as the engine speed increases. Gasoline is a bit dumb and takes a little time between throwing a spark at it and when it peaks the cylinder pressure. So you throw the spark at it sooner as the engine speed increases. But only to a point, where you throw the spark in before it is compressed enough and it no longer needs to be thrown in sooner.
The vacuum advance is to compensate for the lower cylinder pressure at cruising speeds/loads. Since the cylinder pressures are not spiking at part throttle cruise like they do at full throttle you pull the spark in a little sooner to compensate for the lower pressures and the slower burn speed. Again to peak that cylinder pressure at or just after top dead center.
Distributors will have different curves. How much mechanical advance and how quickly it comes in as RPM increases. Stock distributors tend to be conservitive in case you are running a weak tank of fuel, weather is off, etc. Play it safe and not try and peak the power numbers. Performance distributors tend to take more risk and go a little further with the advance and come in sooner. You can tune most any distributor to behave differently. Weights, springs, stops. The vacuum advance is tunable as well, usually just the limitation of total advance in aftermarket versions. Factory would tune with different vacuum curves as well. Vacuum advance is mostly there for economy as full throttle there isn't any manifold vacuum for it to change anything.
That is just the advance curve part of it. There is still the triggering method. From the basic points and a varity of electronic triggers (most being magnetic). Often based on stock parts from Ford or GM.
Points don't need a module, but any of the other triggers will need a module of some sort to look at the signals and power a coil on and off to make the spark. These can be separate, or built into the distributor.
Marketing will put names on the systems. Aftermarket will have there offerings as well, but all based on the same. You can get great (or horrible) results with any of them. Sometimes replacement parts are difficult to get (typically aftermarket proprietary stuff like a Mallory Unilite). And some stuff is super common from any parts store.
I prefer stock parts that are economical and easy to replace if needed. Having had a dead truck in the driveway with a bad speciality part is bad enough, at least it was at home. I could wait days for a new part. So I switched to parts store stuff. Anything that dies can be picked up at a parts store in stock or if a bad parts store, the next day.
