Interesting! What would be the proper terminology for a coil designed to work with a ballast resistor, and one without?
To be perfectly honest, I don't know. In the engineering world, we have all the necessary electrical specs for coils/inductors, and that tells us what the inductance is (the main ingredient for storing energy), and it will tell us other stuff like the dielectric strength (what maximum voltages the windings can tolerate), or peak current/wattage to keep from burning up the wires/windings (and a few other boring details).
But, in the automotive world, those specs aren't always available. You (and I) frequently have to just use some rules of thumb, experience, and common sense. No ignition coil is going to be ruined just by hooking it up to 12 volts, as this is nothing compared to the 150-300 volts that the primary windings experience/endure every time the points open and the plug fires. The main issue to always keep in mind is the current level/magnitude in the primary windings. If you have a points setup, a decent rule of thumb is to keep the peak current in the 4 amp range. This prevents the coil from turning into a toaster oven if you leave the ignition on when the points happen to be closed. If you have an electronic switching system/module (that doesn't require a ballast resistor), you can generally run the amperage up a touch (5-6 amps), as most decent ignition modules will minimize the necessary dwell time to charge the coil, keeping the coil power-dissipation/wattage from getting excessively high.
Cliff notes: If you're running a 6v points system in a vehicle, most coils will work fine without a ballast resistor. If you use these same coils in a 12v points system, it's best to run a ballast resistor to keep the primary current (and wattage) from going too high. Electronic ignition systems (that don't use ballast resistors) can run higher amperage in the coils because the duty cycle (and internal wattage) is generally lower.
(Well, this certainly ended up being a longer answer than I intended.)