Frank,
Much confusion exists..your thoughts are correct.
A. Single wire alternator. One wire out marked BATT. Special internal regulator that does special stuff.
B. Three wire alternator. Output wire marked BATT. Internal regulator too, not quite as special as alternator A. #1 wire to voltage source to energize field and start unit
charging. #2 wire to system to sense system voltage.
C. Three wire alternator. Output wire marked BATT. NO INTERNAL REGULATOR. Wire marked R goes to voltage regulator on firewall, tab #2. Wire marked F goes to voltage regulator on firewall, tab #F. The plug (DA) is usually different than alternator B so you can't mix them up. Sometimes the case is marked 1/R & 2/F.
Three units that look similar..ONE uses a external regulator.
When the dust settles there will be plenty of advice on how to hook your alternator up.
Stuart