Need some electrical help with my ‘68 Plymouth Valiant 100

The alternator makes and alternating electric current (AC), but the car uses non-alternating current (DC).
It is cheaper and easier to make generators for AC than it is for DC, and they work better, so that's what they use now (before the advent of small, reliable, cheap diodes, this wasn't the case, so before the early '60s, cars used DC generators).
It's an example of a genuine technological improvement. They happen.

Alternators, generators, and electric motors (fan motor, starter motor, your vacuum cleaner, cordless drills) all work on the same principle, that a magnetic field crossing a coil of wire makes an electric current (or an electric current acting on a magnet creates force). Some motors or generators are "permanent magnet" types, which get their magnetism from regular old magnets, they type that hold the kitchen cabinets closed, or whatever. Magnet technology has genuinely improved as well over the past few years, so now you can have strong permanent-magnet motors and generators (all those "Brushless!" DeWalt / Milwaukee / Makita cordless drills, etc.), but in the "good old days," permanent-magnet motors and generators were crap because the magnets just weren't strong enough (I suspect it's why the cordless-drill folks advertise "Brushless!" rather than "Permanent Magnet!").

So, all factory-original alternators that I know of (there are some permanent-magnet aftermarket motorcycle alternators now) use electromagnets to make their electricity.
The alternator has a rotor and a stator.
The rotor rotates, the stator stays still.
The windings of the rotor are connected to the outside world with carbon brushes (actually, chunks) that press against brass commutator rings.
When you start the car, the regulator allows a bit of "exciter" current to flow through the rotor, which creates initial magnetism, and as the alternator spins it begins to make current from the stator windings, and the voltage increases.
Once the voltage reaches the regulator's setting (about 13.5 to 14.3 volts), the regulator starts to regulate, limiting the current it feeds to the rotor through the brushes.
Less rotor current = less rotor magnetism = less current generated (alternated?).
You turn on the headlights or the blower, voltage goes down, rotor current goes up, voltage goes back where it should be.
Motor revs faster, voltage goes up, rotor current goes down, voltage goes back where it should be.
You get it.

In our context (I am not an electrical engineer), an alternator with a higher output will need to draw more current for its rotor ("Field Current"), so a regulator designed for a 30A alternator probably won't work (for very long) with a 60A alternator.
HOWEVER, a regulator for a 60A alternator should work just fine for a 30A alternator, as it will feed just enough current to achieve the desired voltage.
Because of this, the average parts supplier, rather than make two different regulators (which both cost the same to make), will just make one, specified as 60A, but it will work for both 30 and 60A alternators.

So a 60A regulator that is otherwise the same should work fine.

BUT, as an aside, using a 60A alternator in a car designed for a 30A alternator could cause trouble ("trouble" = "fire") because the car's charging wiring, including wiring to the ammeter in the dash, is not large enough to handle the increased current.
But that's a subject for about a hundred other pre-existing threads.

- Eric