Montage

Cuts alternating back and forth between two actions happening at the same time in different places.

This is for a motion graphics video. Edit [scene] with a "Cross-Cut" (also called parallel editing or intercutting): cut back and forth between two actions happening at the same time in different places.
Let both actions keep moving forward while they are off screen, so each return picks up later than where it left — unlike a cutaway, which leaves the main action only once and comes back.
Fit the sequence into [duration], and shorten the pieces toward the end if the tension should build.

A foreground object, such as a wall, a person or a passing vehicle, crosses the lens and hides the cut to the next shot.

This is for a motion graphics video. Join two shots in [scene] with a "Natural Wipe" (also called frame blocking or an invisible wipe): a foreground object passes right in front of the lens and the next shot is already there behind it.
Keep the changeover hidden under the object the whole way across, so the object itself seems to wipe the old shot off — unlike a plain wipe there is no drawn edge, and unlike an invisible cut the viewer is meant to see that the scene has changed.
Run the pass over [duration], with the object moving at a steady, natural speed.

The outgoing shot peels or turns away like a page, uncovering the next shot behind it.

This is for a motion graphics video. Join two shots in [scene] with a "Page Peel" (also called a page curl, or a page turn when the whole side lifts): the outgoing shot lifts from one corner and peels away like a sheet of paper, uncovering the next shot lying underneath.
Show the back of the page as it folds over, and keep the shot underneath still — unlike a plain wipe, the old picture reads as a physical sheet being lifted off.
Run the transition over [duration], easing in as the corner lifts and out as the page leaves the frame.

An instant jump to a tighter frame of the same subject along the same line, with no zoom travel between the two sizes.

This is for a motion graphics video. In [scene], use a "Punch In" (also called a cut-in or axial cut): cut instantly to a tighter frame of the same subject along the same line.
Show no zoom travel between the two sizes and let the action carry on without skipping time — that is what separates it from a zoom and from a jump cut.
Fit it into [duration], and put the cut on the word or detail that should get the emphasis.