What we're calling an alternator here is just a certain type of generator. In the UK they are all just "dynamos."
The old "generators" on tractors made AC just like the modern day "alternators." The difference is - the old "generators" use brush placement to select just a fraction of the electrical pulses made and send it through the brushes as DC current. Much of the power generator is wasted. Thus the reason why they are big for the low output the make.
A modern day "alternator" type of generator uses all the AC it makes and sends it through full-wave rectifiers so it's all converted into DC. Also the brushes do not carry any of the output power.
The old cars that did not run when the battery got unhooked did so because of the way the mechanical regulators were wired up. It had nothing to do with the old brushed generator itself. The old brushed generators were better able to make DC power all on their own due to residual magnetism. The newer tech "alternators" mostly rely on 12 volts of "exciter" current fed to them to create enough field magnetism to charge. That being said - alternators also have a bit of residual magnetism and some can self-start just like the old generators if spun fast enough.