Having someone's back is an idiomatic expression meaning that you're watching out for that person, basically taking care and protecting that person from harm.

Backing someone up is also an idiomatic expression meaning that you will support that person in word and deed.

Look out or backs you up, supports you in whatever choices or decisions you make, protects you from harm in the world as well as protecting you from harmful people. Sticks up for you when or doesnt allow others to or are talk/talking about you

when you have a friend that would do you a solid or mutual respect