To be fair, calling it vibrato is also not completely accurate, since vibrato typically refers specifically to regular oscillating pitch (e.g. in singing, or bowed string instruments)

The Bigsby Vibrato was well suited for that type of effect, slight pitch oscillation, but in practice it was commonly used to just bend notes down, or down and back up (often as part of a melody and not just an effect), as opposed to actual vibrato (see Duane Eddy for example, or even Chet Atkins, who would play vibrato with his fingers, but use the Bigsby to bend down notes sometimes)

The Fender design was not really any better for vibrato (arguably it's worse than the Bigsby for that), but you could use it to do a lot more controlled bends and other effects with higher tuning stability and much wider pitch range.

The term tremolo itself has never referred strictly to changing volume either - it simply meant "trembling" effect, which could be achieved with different techniques on different instruments, sometimes by rapidly alternating between 2 pitches so achieve it, and sometimes by repeatedly playing the same note at the same volume (which is how tremolo is played on a classical guitar)

In this sense, you can use the trem/vibrato/whammy/whatever bar on a modern guitar to achieve both vibrato, tremolo as well as many other effects (dives, bends, whacks, what have you) - and calling it either vibrato or tremolo really belies the range of effects the device enables.

Language moves on - everyone now knows what a "trem" is, this whole tremolo/vibrato controversy is really just an artifact of the internet age, where many people feel a strong urge to right the perceived linguistic wrongs and "educate" others as soon as they "TIL" about them :) (e.g. see what happens whenever the word "decimate" comes up)