Metric Modulation
This is a unique application of a polyrhythm, where a pulse is alluded to and then adopted as the new time signature. For example, if you play quarter-note triplets in 4/4 time, you are playing a polyrhythm. If you abandon the 4/4 pulse and use the triplets as the new pulse, then you have modulated to 6/4 meter at a new tempo. And you can go the other direction as well: 6/4 to a hemiola (2:3) to 4/4.
Metric Modulation: 4/4 to 6/4
Asymmetrical Phrasing
Similar to a cross rhythm, this technique uses two or more phrases of different lengths rather than a standard phrase, for example, playing a bar of 5 beats and a bar of 7 beats rather than 3 bars of 4. This is a technique used in some jazz heads. Have a listen to “Straight No Chaser” by Thelonious Monk or Sonny Rollins’s “Oleo” for asymmetrical phrasing applied to melodies.
Asymmetrical Phrasing: 5 + 7
Rhythmic Displacement
This is not technically a polyrhythm, but the effect is somewhat similar. Say you play a simple rock rhythm: 8th notes on the cymbal, 1 and 3 on the bass drum, 2 and 4 on the snare. If you then switch to playing 1&, 3& on the bass drum and 2&, 4& on the snare, you have displaced the pulse by a half a beat, giving the impression that the down beat is no longer where it used to be.
Of course this is not an 'official' interpretation of these terms. I just find that they work for me and help me to understand and apply different polyrhythmic ideas.
Unpacking Polyrhythms Part 1 can be found at http://tinyurl.com/jj7nppy
(http://drumyoda.blogspot.ca/2016/12/unpacking-polyrhythms-part-1-basics.html)