But not a useful answer to someone asking the question… they're simply going to respond with "What's timbre?" and if you answer is something like "It's what makes an A sound different on different instruments", they're not going to be satisfied.

The question is clearly not, "what's the musical term for why instruments sound different when playing the same pitch?" (timbre) it's, "what is the fundamental reason for that?" — and for most people, they have a mental model that an instrument plays a single frequency, so you have to show them that that model is broken, and then it becomes very clear, very fast what is going on.

And timbre is itself technically defined as all the aspects of a sound that are not pitch, loudness, or location.

So, it doesn't really explain anything. It's kinda circular. Timbre is itself the word for "sounding different" (without being different in pitch, loudness, or location).

My simple answer: "different frequency spectrum + consistent patterns of change over time in spectrum, loudness, and/or pitch"

E.g. it's not the loudness of trumpet vs piano, but it is partly the fact that trumpet doesn't consistently have the loud to quiet fade timbrel temporal pattern of piano