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When they say that two people or two instruments harmonize, does that just mean that they're singing/playing in the same scale?

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I'm familiar with this meaning:

the chordal accompaniment to a line or melody: using chords and melodies together

(Wikipedia)

So there's more to the definition than simply playing in one key. The word refers to a specific relationship between chords and melody. To harmonize is to play notes with melody.

Moreover, the notion that the notes must all be drawn from the same key isn't even necessary. Atonal music contains harmonization in a broad, literal sense of the word. These harmonizations may not fit within traditional tonal/functional harmony, and so the additional notes that are played together may not all come from the same scale. But despite this, atonal music can still have a melody and notes that are played with the melody--it can still have harmony.

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Generally, yes, notes used in harmonies will be diatonic - as in belonging to a particular scale or key. But - some harmonies are a better fit if they relate to the chord underlying that particular bar. So, in key C, for example, during a bar with an F chord (IV) there might be a better fit for a harmony with Bb; or in a G bar, an F#. And if a modulation is about to occur, the harmony notes may well be from the new 'key'. As in , still in C, going to Am, there could be a G# as the harmony note, and, as we know, G# isn't diatonic to C.

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