How to use the wrong alternator?

This post and question is merely out of curiosity...

I fixed my alternator problem, so my question now is merely because I'm curious: in my effort to replace an alternator I tried to find information on how to replace a 2 pin alternator with a 4 pin alternator.

I spent a good deal of time searching the internet, but could't find the solution to my problem. So I ended up dismantling the broken alternator and fixing it. It now works, so that's good.

However, I'm curious to know how to actually convert one.

I found some people on the internet explaining that they ran wires to places like the car's computer, which sounds like you would need extensive knowledge of how that specific electrical system works.

And I found that you can buy simple wire adapters online that fit between the alternator and the original wiring harness. However, I couldn't figure out how to find the specific adapter for my alternator and car. And I was also unsure if I needed to do something more complicated than simply using an adapter.

Alternators have a varying number of pins for the connector. I've seen 4, 3, 2, and 1 pin alternators. Possibly there are 5+ pins on some, I don't know.

My question is: can simply using an appropriate adapter work for any car alternator to replace any other car alternator? (Assuming the alternator has the same voltage, and can put out at least the minimum required current.) Or do some cars require something more extensive than simply using an adapter?

Thank you.