C major comes from a major scale. C minor comes from a minor scale. The difference is that a Major triad has a natural 3rd where a Minor chord has a -3rd.
C major and C minor are related keys that have the same tonal center, but different key signatures: C major has no sharps or flats (an empty key signature)and C minor has 3 flats (Bb, Eb, Ab). The C major and C melodic minor scales are spelled out in the other answer. The C natural minor scale stays within the 3 flats key signature and the C harmonic minor scale has a raised 7th (B natural). The sound of the two keys can be simplistically described by saying C major sounds bright and C minor has a darker more melancholy sound.
The pitch set.
All major keys follow an interval pattern of M2, M2, m2, M2, M2, M2, m2 (where “M2” means “major second,” and “m2” means “minor second”). So in the key of see, the pitch set is:
C (M2) D (M2) E (m2) F (M2) G (M2) A (M2) B (m2) C…
All minor keys begin with an interval pattern of M2, m2, M2, M2, M2… then differentiate slightly going forward. Let’s keep it simple and use the natural minor scale, which invokes no accidentals (alterations time the scale):
C (M2) D (m2) E♭ (M2) F (M2) G (M2) A♭ (M2) B♭ (M2) C…
So the difference is the pitch set, or the specific collection of pitches belonging to a specific tonality (key).