Cinemagraph

Moving footage suddenly stops on a single frame that is held like a photograph; differs from Bullet Time because nothing continues to move.

This is for a motion graphics video. Stop the action in [scene] with a "Freeze Frame" (also called a stop-frame or hold frame): the moving footage halts on a single frame and holds like a photograph.
Nothing at all should move during the hold, neither the subject nor the camera — if the viewpoint keeps travelling around the frozen moment, that is bullet time.
The whole beat lasts [duration]; cut into the hold abruptly, mid-action, and leave it long enough to read.

Video compression is exploited (I-frames removed) so the next clip's motion drags and melts the pixels of the one before it, producing smeared, bleeding blocks.

This is for a motion graphics video. At the cut between the two shots in [scene], use a "Datamosh" (also called datamoshing): instead of switching cleanly, let the old picture stay on screen and be pushed around by the motion of the new shot, as if the compressed video had lost its keyframe.
The leftover image should smear and bleed in blocks along the direction things move, melting away piece by piece until the new shot is fully there — a slow melt at a cut, unlike a glitch, which tears for an instant and snaps back.
Let the melt play out over [duration], then leave the new shot clean.

The picture wavers as if seen through hot air or water because pixels are pushed around by a moving noise map.

This is for a motion graphics video. Add a "Displacement Distortion" (also called heat haze, heat shimmer or turbulent displacement) to [scene]: make the picture waver as if seen through hot air, by pushing its pixels around with a noise map that keeps drifting.
Everything stays where it is and only bends and wobbles softly in place; the shot does not change, which is what separates it from a ripple dissolve.
Keep it shimmering for [duration], with the noise rising slowly so the wobble never repeats or freezes.

Copies of earlier frames are blended behind the current one so a moving subject leaves a fading trail of itself; differs from Motion Blur in that the copies stay distinct instead of smearing continuously.

This is for a motion graphics video. Add an "Echo" (also called ghosting, trails or motion trails) to the moving subject in [scene]: copies of its earlier frames linger behind it and fade away.
Each copy should stay a separate, readable ghost stepping back along the path, fainter the older it is — a continuous smear would be motion blur.
Run it over [duration], and let the trail catch up and vanish once the subject comes to rest.