The major chord with additional minor 7th is also called dominant 7th chord or just V7, because as a diatonic chord it appears only on the 5th scale degree, the so called dominant. Based on a C major scale that would mean you go to the 5th G and stack 3rds over it (G, B, D, F). The result is a G7 chord, a G major chord plus a minor 7th.
A C7 has the notes C (1), E (3), G (5) and Bb (7). The 5th is sometimes omitted, especially when the chord is extended with tensions (like 9 or 13) or altered tensions (b9,#9,b13). The #11 comes normally with non-altered chords and therefore has a special role.
Resolution: Between the 3rd and 7th of the dominant 7th chord you can find the interval of a diminished 5th that provides a tension that is resolved in the chord of the 1st scale degree, e.g. C7 → Fmaj7.
Secondary and minor dominants:
Sometimes other chord types are changed to dominant 7th chords before they resolve in a chord a 5th below. Instead C Am7 Dm7 G7 for example sometimes C A7 Dm7 G7 is played. Am7 can be changed to A7 here, because it resolves to Dm7 like a V7 chord to the first scale degree.
The most common secondary dominant is the dominant of the minor scale. The m7 chord on the third scale degree is changed to a dominant chord and resolves to the minor chord on the sixth scale degree (parallel minor). So e.g. in C major (= A minor) you play E7 → Am7 instead of Em7 → Am7.
C Altered: C7alt is a universal notation for all C7 chords with altered tensions. You can decide by yourself, which one you choose, e.g. C7(b9), C7(#9), C7(b13), C7(b9,b13).
In the basic form of a blues scheme you can find a progression of just V7 chords, without any direct resolution from V to I. It’s very interesting that one blues scale (minor pentatonic with additional b5) can be played over al those dominant chords.
The theory of dominant seventh chords (application, extensions, substitutions, appropriate scales for improvisation) can reach a high level of comlexity.