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Keys vs scales is like the chicken and the egg. They are so interrelated, its almost impossible to speak of one without referring to the other. A scale is a collection of notes. A key refers to what scale a song is based on. As mentioned, the key also establishes the tonal center of a song. Everything in the song is related to the key.
As Jeremy says, the word "key" implies a tonal centre, or ruling note. It's a matter of sound, not just theoretical definition. (The latter derives from the former.)
When something is "in the key of E", it means E is the "tonic", the point of rest that the music will end on - probably at various points in the tune, but almost always at the very end.
Keys can be major or minor.
A change from E major to E minor is not a "change of key" (because the keynote is still E); it's a change in "tonality". A change from E major to F major is a change of key.
A "scale" is (essentially) merely a collection of notes. There are many types of scale other than major and minor. There is usually a lower reference note from which the scale degree structure is measured. Eg, "major scale" means a specific set of intervals measured from the "1", the bottom starting note. But the set of pitches defined might be applied in many ways.
Eg, normally one note is specified in the name - eg "C major scale" - but that may not mean a keynote. Eg, the phrase "C major scale" can refer to the notes ABCDEFG in any order or application. The usual assumption (out of context) would be that C is the keynote, but we might refer to "D dorian mode" as "C major scale with D as keynote".
It is often hard to draw a definite distinction between the terms. Eg, the "key signature" on a piece of notation doesn't actually specify a key - only a collection of notes (scale). Eg, a 2-sharp key signature specifies the notes A B C# D E F# G. Those notes (that "scale") could be used for either the D major key or B minor key - a different keynote (tonic) in each case.