Two notes which are a fifth apart will have a 3:2 frequency ratio. If one drops the upper note by an octave, the ratio will be 1.5:2, which in normalized form would be 3:4. When distortion is applied, frequency ratios become far more important than musical intervals.
Playing a note on a normal guitar string will actually generate many frequencies, all of which are generally very close to being multiples of the fundamental. Distortion will generally turn a set of frequencies into a broader set which may contain any frequency that is the sum of any combination of positive or negative multiples of frequencies present in the original. For example, if one fed into a distortion box a signal consisting of pure 100Hz and 111Hz tones, the output could include 200Hz, 222Hz, 211Hz, 311Hz, 122Hz (+2 x 111 + -1 x 100), 89Hz (+2 x 100 + -1 * 111), and many other frequencies. Rather a jumbled mess.
If two tones are played a perfect fifth apart, their frequencies will have a 3:2 ratio. This means that all multiples of them will be multiples of half the lower frequency (or a third the upper), and all combinations of multiples will likewise be multiples of half the lower frequency. The net effect is that feeding a power chord through a distortion box, will yield a result similar to putting a note an octave lower through some (possibly different) kind of distortion box.
If the tones are played a perfect fourth apart, their frequencies will have a 4:3 ratio. This means multiples of them will be multiples of 1/4 of the upper frequency (or 1/3 the lower). The effect will be similar to putting through a distortion box a note two octaves below the upper note, though unless one is using the middle or upper ranges on a guitar, that "resultant" tone will be too low to really be perceived as a pitch. Further, the lower of the tones will compete for "recognition" with that resultant, so the sound will be much less clear.