What is the difference between a scale, a chord, and a key?
A scale is notes in sequence, a chord is notes at once, and a key is the gravity system that makes one note home for both.
A scale is a set of notes played one after another, like an alphabet. A chord is a few of those notes played at the same time, like a word.
A key is the bigger idea: it says which note is home and which scale supplies the material, so it governs both the scales and the chords a song uses.
Scale: an ordered collection of pitches defined by its interval pattern (major = W-W-H-W-W-W-H). Chord: typically stacked thirds from a scale, sounded together (C-E-G). Key: a tonal center plus the scale built on it, establishing hierarchy: which notes are stable, which pull.
The three interlock: the key of C major uses the C major scale, and its family of chords (C, Dm, Em, F, G, Am, Bdim) is built by stacking thirds on each scale degree.
Confusion arises because "C major" names all three: a scale, a chord and a key. Context decides: play the C major scale, strum a C major chord, write a song in the key of C major.
A key is more than its note set: A minor and C major share every pitch, yet they are different keys because a different note carries the gravity. Tonality is a hierarchy (tonic, dominant, subdominant functions), not a collection.
This is also the scale-versus-mode question: D Dorian versus C major is the same seven notes with home moved to D. What changes is which tones feel stable and where phrases resolve, which is audible, not notational.
For the practical musician: think key first (where is home), scale second (what is the palette), chords third (which stacks the palette offers). Improvisation questions like "what scale fits this progression" dissolve once the key is identified.