Correct.
The way I learned to distinguish modes was the "LIMDAP system" (I don't know if this is a real system, just what I nicknamed it. I extended it it to LIMDAPL -- rhymes with "Snapple" -- the reason for I will explain in a moment). This was from my theory class in college.
The LIMDAP refers to an order of modes: Lydian, Ionian, Mixolydian, Dorian, Aeolian, Phrygian (add Locrian for LIMDAPL).
The idea is a logical movement left-to-right (but we'll go up-down due to formating on the web) based on raising and lowering of degrees. Taking a parallel approach (all with C as tonic):
Lydian: C D E F# G A B C
Ionian: C D E F G A B C
Mixolydian: C D E F G A Bb C
Dorian: C D Eb F G A Bb C
Aeolian: C D Eb F G Ab Bb C
Phrygian: C Db Eb F G Ab Bb C
and also
Locrian: C Db Eb F Gb Ab Bb C
The reason they left Locrian out was because, according to my teacher, Locrian can't be used because of its diminished 5th... it's too unstable, or some nonesense like that. Horse-hockey as far as I'm concerned.
But, do you notice a pattern? Notice the progression of raising and lowering degrees from mode to mode? Once I wrapped my head around that relation, I came to know modes like the back of my hand.