Transition types

Cut

The most common transition — an instant change from one shot to the next. The raw footage from the  camera contains cuts between shots where you stop and start recording (unless built in transitions are used) In music videos the vast majority of transitions are cuts.

Mix / Dissolve / Crossfade

These are all terms to describe the same transition — a gradual fade from one shot to the next.
Crossfades have a more relaxed feel than a cut and are useful if you want a meandering pace, calm mood, etc. Scenery sequences work well with crossfades.
Crossfades can also convey a sense of passing time or changing location. i.e one shot of walking to a place to another being in the different location/ position

Fade

Fades the shot to a single colour, usually black or white. The "fade to black" and "fade from black"  usually signal the beginning and end of a music video.
Fades can be used between shots to create a sort of crossfade which fades quickly to white before fading to the next shot.

Wipe

One shot is progressively replaced by another shot in a  pattern. There are many types of wipe, from straight lines to different shapes.
Wipes often have a coloured border to help distinguish the shots during the transition.
Wipes are a good way to show changing location.

Other Digital Effects

These effects include colour replacement, animated effects, pixelization, focus drops, lighting effects, etc.