DT 770 Pro is available with 32, 80 and 250 ohms transducers, these also differ in application:
the 32 ohms DT 770 Pro works great with computer soundcards, audio interfaces, portable recorders and players (mobile phone, tablet, handheld recording device, etc., units, powered by (rechargeable) batteries or external supplies), also with instruments like digital piano, synthesizer or instrument amplifiers (e. g. for guitar).
DT 770 Pro with 250 ohms is suitable for stationary sources like mains powered studio monitor controllers, hifi-amplifiers, headphone amplifiers, etc.. Both versions, 32 and 250 ohms are based on very low mass, so called: underhang voice coils, which can reproduce enormous details with low distortion. For the lower impedance, we use slightly thicker - and heavier - wire for the coil, therefore, it plays louder with lower supply voltages (from mentioned units) as the 250 ohms version.
80 ohms DT 770 Pro is optimized for very high listening levels in a recording studio, for example musicians, playing an instrument, etc.. You normally can find very high power headphone amplifiers here and achievable level is more important than the last bit of sound quality. This transducer uses an overhang voicecoil, which is longer than the air gap. Its larger surface increases the electrical power handling (better cooling) but its higher mass results in a different distortion behaviour.
finally, DT 770 M is a specialized version of DT 770 Pro 80 ohms for very loud environments: due to its stronger headband, totally closed earcups and special earpads, it gives a far stronger isolation from and to the outside than regular DT 770 Pro phones, but compromises sound quality and (long term-) wearing comfort.