In order to drive any loudspeaker you need power. It isn't current vs voltage- if you can't make the voltage you can't make the current.
So the conversation is really about the output impedance of the amplifier driving the speaker. If it is very low with respect to the speaker, the amplifier can act as a voltage source since the amp can make constant voltage with respect to load impedance.
If the output impedance is very high, usually a multiple of the load impedance, the amplifier is a current source meaning the amp will make constant current regardless of the impedance of the speaker. The only speakers I know of needing this sort of drive are open baffles with some very specific drivers.
If the output impedance is close to or slightly less than the impedance of the speaker, the amp is likely a power source.
To create a voltage source you either need an inherently low output impedance such as is available from certain semiconductors, and/or you need enough voltage feedback to cause the amp to behave as a voltage source (though servo action of the feedback voltage) even if its output section is relatively high impedance otherwise. This is why tube amps can behave as a voltage source. The idea behind voltage drive is plug and play- no having to adjust the speaker to match the voltage response of the amplifier as with the prior art.
To create a current source the amp will need to have current feedback rather than voltage feedback. Usually this is done by placing a small resistance in series with the output load, over which a voltage drop will occur. This voltage is then fed back into the amplifier and will cause the output impedance to increase, again according to the rules of control (servo) theory.
To create a power source you either use a tube amp with no feedback (which will approximate a power source) or run both current and voltage feedback and balance the two exactly against each other. This was the predominant method of loudspeaker drive until the late 1950s when EV and MacIntosh introduced the idea of an amplifier being a voltage source and the speakers thus 'voltage driven', that latter bit in quotes because its a term with a meaning. This idea took a good 20 years to take over the industry.
There are still loudspeakers that are power driven (Power Paradigm) as opposed to voltage driven (Voltage Paradigm) made today. The former are arguably less than 1% of all speakers made.
I think you can ignore Wolf von Langa's background links since they are exactly that, unless you really want to delve into a lot of stuff that won't seem directly related to audio. FWIW, field coils are a lot different from voice coils in that they are used to produce a magnetic field of constant level. I see their advantage as allowing a cone speaker to have similar speed to an ESL, on account of the magnetic field not sagging as current is applied to the voice coil. To do that though requires some form a regulation as discussed earlier.