They are mutually exclusive. A game can contain elements of both. An rpg may have some elements of story involved. If these elements require players to operate outside the role being played and effectively play the role of storyteller during actual play then the game has morphed into a storytelling game. This becomes even more so if the stated design of the game is to create collaborative stories instead of experiencing the game from within a chosen role.
No they're not. Creating stories is a function of roleplaying games. If everyone sits down to a game and plays their role, a story is created. A given game might not care about the quality of that story, but it still exists. Being a story creation game is a byproduct of being a roleplaying game.
Relate to me what a game session would be like that did not create a recognizable story. Here's a hint to help you, a story means 'stuff happens to possibly imaginary people. There's a start, a middle, and an end.'
Your entire idea of a division between roleplaying and story creation is fallacious. Every RPG session ever played created a story. You can just say you don't like mechanics that try to make the created story better, you don't have to categorize them as some other hobby entirely. Its okay.