Do I get it right that if I 'get through' things I make some effort or struggle with something? But if I 'get over' things I always win and it always ends up well?
Your idea regarding "'get through' things" is basically correct. You are working through some situation with extra effort.
But when you get over things, it means to move past something that is needlessly slowing you down. For example:
I know you really miss your ex-girlfriend. But you really need to get over it and fine someone new.