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A month or two ago, I participated in a school music programme, where I was playing guitar. The chord progression I was playing was in the key of C. Then our music teacher comes, and asks in which SCALE we are playing the song. I - without thinking much - told her that it's in C Major.

But now that I think of it, I had used the terms 'scale' and 'key' interchangeably, which obviously isn't very correct.

A scale is a collection of notes, with specific intervals (for example, the Major Scale is made from the intervals R, Major 2nd, Major 3rd, Perfect 4th, Perfect 5th, Major 6th, Major 7th, Octave).
But a KEY, is basically every note in the corresponding scale, counting notes that span MORE than a single octave. For example, the key of G Major contains the notes G, A, B, C, D, E, F#, but in every octave.

Then what should I have said to the teacher? Were the teacher's wordings inaccurate? Because it really seems like she was using the terms 'scale' and 'key' interchangeably.

(By the way, I have another such programme coming up, and we have rehearsals from tomorrow. Wish me luck :)

(EDIT: I don't know a lot of music theory, and I live in India, if either is relevant)

Then our music teacher comes, and asks in which SCALE we are playing the song.

That's not usually the way people use the vocabulary. People talk about a song being 'in' a key, not 'in' a scale. Maybe she just made a brief slip of the tongue, or maybe she was assuming that what you were playing would be restricted to a particular scale for some reason, and was focusing the question towards that.

Is there a different definition of scales in Indian classical music? (from your comment)

There are definitely scales in Indian music that wouldn't relate strongly to the Western key system - so if she thought you might be using one of those, yes, that could be a reason for her phrasing.

But now that I think of it, I had used the terms 'scale' and 'key' interchangeably, which obviously isn't very correct. A scale is a collection of notes, with specific intervals (for example, the Major Scale is made from the intervals R, Major 2nd, Major 3rd, Perfect 4th, Perfect 5th, Major 6th, Major 7th, Octave). But a KEY, is basically every note in the corresponding scale, counting notes that span MORE than a single octave. For example, the key of G Major contains the notes G, A, B, C, D, E, F#, but in every octave

I don't think that's quite right. You could talk about a scale that spans more than one octave - it's just that Major scales are octave repeating, so we don't usually need to.

I would say that the difference between a scale and a key is that a scale is a collection of notes, while a key is a more general description of the tonality of a piece. So you can have a piece in the key of C major that uses notes that are not in the scale of C major.

Nevertheless, the two concepts are very closely related, at least when it comes to the major/minor system.

Then what should I have said to the teacher?

Nothing confrontational, of course - just smile and be polite :).

I suspect that this is a question of translation, probably more between musical systems than between languages. In Indian music, pieces are analyzed in terms of raga and thaat. These concepts are similar to European melodic modes, which nowadays are largely confined to two: major and minor, with some notable exceptions. (Formerly there were eight: Dorian, Phrygian, Lydian, and Mixolydian, plus the Hypo- variants of those four.)

Because Indian music is analyzed according to concepts that can be (approximately) translated as scale, it seems natural for an Indian musician to ask about a piece's "scale" rather than its "key." For a native English speaker trained in European music, it's a bit odd to speak of a piece's scale instead of its key, but no more than a bit odd. There's no reason to think that "scale" in this sense means anything particularly different from "key."

Additional discussion

Two factors have led to the development of key from the melodic modes. One is the development of harmony, whereby the mode affects not only the pitches used in a melody, but also the pitches and therefore the chords available for harmonic use. Along with this came the development of tonality, whereby the eight modes more or less merged into the major and minor tonalities. (This led to the invention of the Ionian and Aeolean modes, along with their Hypo- variants, in the middle of the sixteenth century, but that theory didn't stick particularly well. The major/minor dichotomy prevailed instead.)

The other element in the concept of key is the development of standardized pitches, whereby the pitch a is around 400 or 450 cycles per second (more recently around 440), and of the twelve-tone system, which allows pieces in any mode to be played on any starting pitch. It is no longer sufficient to say that a piece is "in the minor mode"; we must say that it is "in D minor" or "in F-sharp minor" or whatever else.

So it seems that the Indian concept might be better translated as "(melodic) mode" rather than "scale," but mode in the medieval sense is no longer a particularly common concept in European music, whereas everyone trained in European music knows what a scale is.

Just a thought -
It's common to use a different scale for a lead part then a key which the song is in.
For example, take a blues progression in A major (A, D, E). When soloing over this, you would be typically using A minor scale to sound "bluesy".

You can also be using a pentatonic scale to play over a progression, for example, playing C major pentatonic over a progression in C major key - which would be common in rock.

Should have asked 'Which SCALE NOTES were you using?'

Each major key has one 'set of notes' that constitutes it. A pool of notes, if you like. When put in order, low to high and vice versa, that's a scale. French word echelle sums it up - also meaning ladder. And, after all, we say 'scale a ladder'.

But we never (rarely?) use the words key and scale as synonyms. It might work for majors, as it's the same pool for both, but with minors, it's impossible! And a scale presumes notes which are consecutive in the same octave. Ever heard of a scale using C2, D3, E5, F3, G4 etc..?

Your teacher probably just made a mistake. I don't recall hearing talk about "playing a song in a scale", as if you could decide to play it in another scale. Doesn't make sense. It's "in a key".

Edit: India mentioned. Nevermind this answer. What I said only applies to the narrow field of Western music I've been exposed to.

Music which uses the C major key signature (empty: no sharps or flats) can use a note other than C as the root of its tonality, thereby being based on a scale that is a mode of C major. It is then effectively in the key of that root note, not in the key of C.

For example, music in the key of A which uses the Aeolian scale will use the C major key signature. Chords used in that music will be ones you see in C major music. Similar reasoning applies to music in G using the G Mixolydian scale, or music in D using the Dorian scale.

Therefore, we can't assume that just because it superficially looks like C major, that it really is music "in C".

If the chord progression goes like this: G F C G and the melody emphasizes the G note, such as by starting and ending on it, I would tend to say that the music is in the key of G, using the G Mixolydian scale (which, being a mode of C major can be written with an empty key signature).

You have to analyze the musical structure of the song; how is it using the notes taken from C major? What notes are emphasized? Does the ending resolve to a particular note?

The most important note to which the music gravitates likely gives us the key, and the scale is then the notes of that music arranged in order, starting from that note.