Unless the version string in the kernel and in the module match exactly the module cannot be loaded at all.
There are some exceptons, kernel & modules my be compiled with modversions-option, and this enables that some symbols can be marked to be exported across versions but in practice it's not so useful (and it is quite rare to do so)

So, in practice for a module to load at all it needs to be compiled from the same kernel tree as the base kernel.

Modules, after all, are fully part of the kernel code, just packaged a bit differently so that they can be stored away from the base kernel and loaded only on need.
(and quite handy for developers, instead of compiling and flashing whole kernel when I make a small tweak I just compile the module and load it, no flashing required...)