With standard tuning, the former is called a root position C chord since the tonic (C) is in the bass. The latter is indeed a first inversion C chord. In music theory, a chord with the third in the bass (in this case, the E) is called a first inversion chord, and is notated with a superscript 6. More formally, it is called a 6/3 chord since the chord is constructed with intervals of a third (G) and a sixth (C) above the bass(E) . The 3 is implied, so people just call first inversion a 6. Second inversion has the fifth in the bass, and is called a 6/4 chord (since it is constructed with intervals of a fourth (C) and a sixth (E) above the bass (G). An example of a way to finger a second inversion C chord would be 9787 (or 5787 to double the tonic).