Cringe is the expression of wanting something awkward or uncomfortable to end.
Embarrassment is what you feel when something that would have a negative impact on your social status is revealed to others.
The expression most often tied to embarrassment is cringe, but it can be used in other contexts as well.
If you are afraid of spiders and see someone hold a spider, you may feel safe enough to not feel fear, but instead feel great discomfort. That is cringe.
If an actor in a movie is really terrible, the performance will be awkward, and you may cringe from how bad it is.
If you hear someone play a song on an instrument, but they are hitting the wrong notes, that may cause you to cringe.
Something I find intensely cringy is: https://www.youtube.com/watch?v=ImhfIv5NSqY
It's physically painful for me to watch.