What is the difference between Throw sb under the bus and Stab sb in the back ?Feel free to just provide example sentences.

They both have elements of betrayal, but in different ways.

To throw somebody under the bus, means that there is some kind of big trouble coming, and you shoved them out right into it, so that they get blamed instead of you. Using them as a sacrifice, letting them get the blame or the problems or the harm that was coming, while you can pretend to be innocent and not know anything about it. So that everyone is distracted by the person who got run over by a bus, instead of asking you any hard questions. You put them into harms way, in order to protect yourself or to distract people so you could hide your own mistakes.
It could be a personal betrayal of trust, or it could just be a stranger who thought it was convenient for them to blame you or leave you to take all of the blame, etc. It is used to mean the opposite of loyalty - someone who would throw you under a bus, let you get run over, because it was convenient for them and they didn't care enough about you. So the phrase means that someone was the opposite of loyalty and the opposite of protecting someone.

To stab somebody in the back is more directly betrayal. It is also more personal. And more destructive. Like they went out of their way to hurt you directly and hurt you badly, maybe even trying to destroy you or your reputation or something else important to you. This phrase is mostly used when it feels like someone you trusted, used that trust to deliberately hurt you in a bad way. You trusted them with a secret and they used that information to spread terrible rumors about you. They knew you were working hard for a promotion and they sabotaged it or stole it for themselves. They pretended to be friendly but were actually planning to turn against you, revealing they were never really your friend at all. It is like being suddenly stabbed in the back, because you don't see it coming and only someone you trust would be allowed to stand behind you where you can't see them directly. It is a phrase for the worst kind of betrayal.