Cm chord inversions
Cm/Eb and Cm/G are the first and second inversions of the C minor. This means that the bass tone is shifting from C to Eb or G.
Try in a chord progression
Cm/G - Ab - Bb
Theory of the Cm/Eb and Cm/G chords
Both chords consist of the notes C, Eb, G. The difference is that the order of notes shifts. Eb is the bass note in the first inversion is and G is the bass note in the second inversion.
A comparison between the main C minor and the two inversions can be seen below.
Chord constructionCm x - C - Eb - G - x - x
Cm/Eb x - Eb - G - C - Eb - x
Cm/G G - C - G - C - Eb - G
Guitar versions of the chord
Notes in chordCm C - Eb - G
Cm/Eb Eb - G - C
Cm/G G - C - Eb
Only the order of notes differs
When stumble upon these chord names, you can choose to ignore the alternate bass note and play the regular C minor. It will always sound ok, but it may lack some subtle additions to the sound. Notice that the version of Cm/G presented above is similar with the Cm barre shape with the bass note on the fifth string except that the sixth string has been included.