The progression I IIIm7 VIm7 IV - minor 7th chords
The progression I IIIm7 VIm7 IV is also a variation of the famous I V VIm IV progression. The V chord has been replaced by a IIIm7 chord and we play the VIm chord as a 7th chord now. By the way, the IIIm7 chord contains the V chord - you can consider Em7 as a G major chord with E as bass note.
A very famous song, consisting entirely of this chord progression, is Price Tag from Jessie J.
The diatonic chords
On the staves you can see the chords that belong to the key that has been selected with the buttons above. This time we stack 4 tones in 3rds on top of each other. We end up with the root, a 3rd, 5th and seventh.
The minor chords always contain a natural seventh (7) and we can nearly always play a minor 7th chord (m7) instead of a pure minor chord.
Unlike the minor chords, major chords may also contain a major 7th (maj7). Besides that, maj7 chords and V7 chords have more of an own charakter that has to fit the style of music.
Here the progression I IIIm7 VIm7 IV is played in all 12 keys: