Fade

The outgoing shot fades to a solid color, usually black or white, and the next shot fades in from it.

This is for a motion graphics video. Join two shots in [scene] with a "Dip to Black" (also called a dip to white, wash or washout when the color is white): the outgoing shot fades to a solid color and the next shot fades in from it.
The two shots never overlap, and for a moment in the middle the screen is nothing but the solid color — unlike a plain fade, it carries on into the next shot.
Run the transition over [duration], split evenly between the way out and the way in.

A very brief shot, often one to three frames, jammed into the sequence for a near-subliminal jolt.

This is for a motion graphics video. Add a "Flash Cut" to [scene]: jam a shot lasting only a few frames into the sequence, then snap straight back.
It should register as a jolt more than as an image — unlike a cutaway, the viewer gets no time to read it.
Fit the sequence into [duration], and make the inserted shot differ strongly in brightness from the shots around it so the flash is felt.

One shot is instantly replaced by the next with no optical effect; the baseline every other transition is compared against.

This is for a motion graphics video. Join the shots in [scene] with a "Hard Cut" (also called a cut or direct cut): one shot is replaced by the next instantly.
Put no fade, wipe or any other effect on the cut — unlike a smash cut it is not meant to shock, it is just the plain shot change.
Fit the shots into [duration], and place the cut on a beat or a finished movement so it passes unnoticed.

A cut disguised so the viewer does not notice it, often hidden behind a dark object or camera move to fake one continuous take.

This is for a motion graphics video. Hide the join between two takes in [scene] with an "Invisible Cut": disguise the cut so the footage plays as one continuous take.
Let a dark object fill the frame while the camera keeps moving, cut in that moment, and pick up the same movement at the same speed on the other side — unlike a natural wipe, the viewer should not notice that anything changed.
Fit both takes into [duration], and keep the camera speed steady through the hidden cut.