Yes, a can of worms indeed! I don't think it is worth raising your blood pressure trying to assign the terms "generator" and "alternator" to specific types of machine. The airframe manufacturers use the terms in a haphazard way which gives them practically the same meaning. I do of course agree with the specific definitions given above and they are strictly correct but, in normal daily usage there is no difference in meaning; they are both machines to convert rotary mechanical energy into electricity.
BTW
"So Generators (as in units producing direct current) are definitely not in use in modern commercial aircraft"
Sorry but the Embraer 145 family of airliners has only 28V DC electrical systems and they have 5 "generators" producing 28V DC at up to 400Amps! A great little aeroplane with very simple and reliable systems!
Sorry!!