Well the translation is kind of hard.. but the first one means " He succeeded in escaping ". The second would be " He had the idea of finding ".
Logró comes from the verb Lograr, which means "to be successful in..".
Ocurrió comes from the verb Ocurrir, which means that you had an idea. For example, "se me ocurrió comer" means that I just got the idea of eating.
Hope its clear.
"I managed to get there" would be "Me las arreglé para llegar ahí".
Arreglar is not only to fix something, but also to arrange things.
You can write to me if you have more doubts.