What "mode" is static electricity (lightning?) Is it common-mode, differential-mode? It seems half-way, or "mono"
I'd be careful about trying to box things into human classifications just because. Just because we have classifications for something doesn't mean they exhaustively encompass all, or even most, possibilities between them. Classifications exist not for exhaustiveness, but for usefulness and convenience of communication.
I also believe that differential and common mode don't mean anything without a circuit, since it's all relative to whether it enters the circuit on terminal relative to another terminal, or whether it enters multiple terminals. In other words, if you want to try and classify ESD and lighting this way, then it just depends where the ESD and lighthing travel rather than whether it is ESD or lightning itself. What determines whether it is differential or common mode is not the fact that it is ESD or lightning. What determines it is where that ESD or lightning enters or exits the circuit. It could be either depending on circumstance, or could simply not fall into the nice neat box of differential vs common mode which we use in circuit models (which assume closed loop currents).
For example, if I touch have a charged floating conductor touch it to another metal conductor to re-distribute and equalize that charge. What is that? There's not really a return path. You can model a closed-loop circuit with a return path using the free-space capacitance but that is more forcing a real life situation into a way you can handle it with a circuit where it is more easily worked with so you don't have to work directly with the more complicated physics.
How about if that charged, floating conductor...

touches two input terminals and a ground terminal?
Or what if it just touches an input terminal? Or both input
terminals?
Or just the ground terminal?

A charge equalization happens in all cases with charge flowing in the same direction through one pin, or multiple pins, but there is no return path (unless you consider the free space capacitance model to be that return path that).
Maybe it is differential if charge travels over one-pin and common-mode if it travels over multiple pins, but with no return path, is it really? But consider this: Without a second terminal with charge flowing in the opposite direction to form a return path, your differential choke won't do much for #2 or #3 despite being called differential.
Whatever you call it, it doesn't change what is happening and you design for it. That said, I would assume the free-space capacitance acts as the return more often that not (i.e. there is no real return path, especially one through the pins) so magnetic cancellation that expects a differential current is probably mostly useless.
However, I believe common-mode magnetic cancellation is only slightly less useless because you must hit the same terminals the common mode choke is across at the exact same time. ESD is fast enough to do most of the damage if you do not immediately make simultaneous contact with both terminals on the common-mode choke due to the small window where one terminal touches slighty before the other thereby permitting charge equalization through just one choke terminal. A resistor or single-ended choke with low parasitic capacitance would probably be more effective all around.