like you noticed in the other thread people have different preferences what to call "sync" and what not.
so you could say if WC "synchronizes" something, then it only syncs DACs or ADCs. everything else in a device, such as a software or a tape machine, is only controlled by its DAC.
lets say an analog to digital signal converter constists of a clock, the actual converter and the analog components.
converters all sound the same. the difference in sound quality comes from the accuracy of the clock and the quality of the amplifier.
sending a device an external clock signal means that the external clock can now be used instead of the internal one.
for recording it is okay to put up to 3 DACs in series, which introduces a minimal delay to the WC signal. for other applications you might need "100% sync" and then you have to use a clock multiplier (a splitter - makes 2 or 4 signals out of one)
the WC itself is nothing more than a gate signal / square waveform at samplingrate.
external clock is nowehere really required to operate stuff, except for transmitting signals between devices (which is a pretty 1990 idea)
but for some mid range audio interfaces (motu, behringer, focusrite) it can do wonders to the sound quality. a good clocker or reclocker today is far below 1000 bucks and that is easily justified if you have multiple audio interfaces.