These verbs are almost the same meaning. But there's a difference between them. Both of them mean to be able to do something, for example:
-Eu posso levantar você.
-Eu consigo levantar você.
These examples mean the same thing.
But when you want to say about permission, for example: Eu posso sair a noite, minha mãe deixa. You cannot use conseguir when talking about permission.
I hope you understand, sorry about my English.