O.K, you asked for it! Basically the major difference in a model 61 and a 65 generator is the size wire used in armature windings and how the fields are connected. The 6 volt versions use heavier gauge wire than the 12 volt. In the armature, this allows more turns per winding, which makes the voltage higher at any particular speed of rotation. So, according to electrical theory, a 65 might reach 12 volts at a speed of 600 rpm, a 61 might not make 12 volts until say, 1200 rpm. Those are just educated guesses on voltages and speeds, but probably aren't too far off. For the happy go lucky guy who's twisting the wick, your 61 generator is almost always going to be spinning fast enough to make at least 12 volts and do all the stuff you want electricity to do.
About Fields: They're just electromagnets, wire wrapped around a piece of iron. the more turns around the iron, the stronger the magnet. In a generator, there is a maximum reached where more windings or more current through them, just won't do any good. It's just wasted, the magnet doesn't get proportionally stronger. When H-D made the 61 into the 65, the doubled the voltage, and connected the field windings in series, so that each winding would see the 6 volts it had been originally designed for. An easy, quick, fix.
On the older models like the fan generator, the fields appear to be designed a little differently, so series connections do not give maximum generator output. With the 32E2R I've experimented with, I got the best results leaving the fields connected as they were in stock 6 volt mode. I'm thinking that the fan version will have the same results. The components appear to be similar. Let me make this point clear, it WILL NOT hurt the fields to apply 12 volts to them, it might not be the optimum configuration for 12 volt operation, but it sure beats rewinding your own fields with about 2 thousand feet of very small wire, in a very precise pattern.
One last comment and I'll shut up. My current thinking on 6 volt and 12 volt H-D generators is that a 6 volt generator may be a superior generator for all around use, especially for a tinkerer like me. The 6 volt armature has heavier gauge wire in the windings than the 12 volt model. Personally, I've burned up 3 or 4 65A armatures in the last 15 years, and Zero 32E 6 volt armatures. Now, it's my own fault because I'm building my own electronic voltage regulators,and I tend to play around with voltages, battery types, charging rates, etc, etc. A 65A armature is designed to handle a max of 10 amps output, period. It was also designed to start making 12 volts at a much lower rpm than H-D's 6 volt armatures. The result, they can't take the heat,and burn out if slightly overstressed.
The 6 volt armatures have heavier windings and create less heat from the current passed through them, making them, in my eye, more robust. and harder for me to burn out
The bottom line, if you keep your generator amperage output below what H-D rated them at, you're going to be o.k., no matter what voltage you run them at. If you're eying 150 watt quartz headlights so you can SEE at night, like me, I'm thinking you're better off with a 6 volt generator, that takes a few more revs before it starts making 12 volts, but can "take the heat" , so to speak.