phrygian C
C-Db-Eb-F-G-Ab-Bb-C
Dorian C
C-D-Eb-F-G-A-Bb-C
Mixolydian C
C-D-E-F-G-A-Bb-C
Like Mentioned before the Dorian and Phrygian are both minor and the Mixolydian is Major.
The Phrygian is made up of:
Root, flatted 2nd, flatted 3rd(which makes it minor), 4th, perfect 5th, flatted 6, & flatted 7.
** The only difference between the Phrygian and a Natural minor however is the Flatted 2nd. **
The Dorian is made up of:
Root, 2nd, flatted 3rd, 4th, perfect 5th, 6th, flatted 7.
** The only difference between the Dorian and the Natural minor is the 6th, is not flatted.
The Difference between the Phrygian and the dorian then is the 2nd, and the 6th.
Root, flatted 2nd, flatted 3rd(which makes it minor), 4th, perfect 5th, flatted 6, & flatted 7.
Root, 2nd , flatted 3rd(which makes it minor), 4th, perfect 5th, 6th , & flatted 7.
Mixolydian is the Major Scale (Ionian Mode) just with a flatted 7. This mode is often used in funk!
As to when to apply them. Here is a few ways they can be applied. (Note I said few ways, as not to spark are MODE application debate, and whose way is better)
Okay back to the post.
If you are in the Key of Ab & the 3rd Chord is being played, you can utilize a C Phrygian scale (mode) to create a run, riff, or solo, as long as the C chord is being played. Because the 3rd Degree of the Key of Ab is C, but the C Scale would not apply, there will be certain notes that would not fit... like the D E A & B, instead the Db, Eb, Ab, & Bb would work in that context.
If you were in the Key of Bb, and the 2nd Chord is being played, you can utilize the C Dorian scale (mode) like above because C is the 2nd Degree of the Bb Major Scale.
If you were in the Key of F, and the 5th Chord is being played, which is a dominant chord. The C Mixolydian can be played because of the flatted 7th.
Knowing these modes like funkStrat_97 said can be very useful for fills, and also for finding your way around the fret board... if you find yourself on the 2 of a progression, in a part of the fretboard that you are unfamiliar with... play the Dorian Mode, it will fit
I hope that was clear.