I've always thought the way modes are defined: "play C major from D to D, that's Dorian..." as the "backward" way to get to modes. It's merely a definition. The "forward" way to get to modes is what I memorized: Dorian is the major scale with a flatted 7 and 3; Aeolian is major scale with flatted 7, 3, and 6; Mixolydian is major scale with flatted 7. This is easier to me than trying to figure out, when someone says this is F Lydian: ok, so F is the 4th of C, so it's C major from F to F. MUCH easier to just think: ok, it's F major with a sharp 4. Easier and it makes the harmonic use of modes readily apparent because you're thinking of a tonal center in F, not in C and trying to transpose.
If you spend enough time with it, all of the different ways of thinking about modes (or anything else, for that matter) will make themselves apparent. The ultimate goal is to not think about it at all.