Every key has at least 2 forms: major & (natural) minor
The key of C major (using the major scale) has no sharps or flats, and coincidentally no black notes. On the other hand, the key of C minor (using the minor scale) has 3 flats. Illustration:
C major: C D E F G A B
C minor: C D Eb F G Ab Bb
As you should know, minor starts on the 6th scale degree of the major scale. So, playing in C minor is the same as playing in Eb major.
So, the musician(s) is/are probably switching or playing notes in both C major and C minor. Calling it the key of C gives you the liberty to play in both.
*side information*
This is a good explanation for beginners to grasp. Once you get more experience and gain more understanding, you will find that every note and chord is a part of every key. What keeps you in a certain key is the chord you claim to be 1. As long as you return home at some point, it doesn't matter the musical journey you take.
