To understand the difference between flangers and phasers, a basic understanding of sound waves is necessary. A sound wave will consistently flow from positive to negative. Notes move at a constant frequency. For example: an open "A" string vibrates 440 times per second.
Phasers, originally called phase shifters, produce the effect of sound being played out of phase with itself, by combining the original signal with a delayed signal. Physics tells us when two signals are played out of phase with each other, certain frequencies are canceled out. The result is notches in the sound wave creating the sound effect.
Flangers sound similar to phasers because they too produce notches in the sound wave. Their sound also is created through a delayed signal, generally a few milliseconds behind the original. Audio engineers discovered the effect by touching the flange (outer rim) of the tape reel during playback.
While flangers and phasers have similar effects on sound waves, there is one major difference on how the waves are affected. Flangers create larger numbers of notches in sound waves, and do so at consistent intervals regardless of frequency. Consequently, a flangers have the same effect on high notes as they do on low notes. Phasers produce fewer notches in sound waves, and the phase response is not linear. Therefore, the effect "shifts" different frequencies at different intervals and the effect is more random.