Ideally, they should be the same thing.
If you have the mindset of, "I have this game, now what story am i going to tell alongside it", you're doing it wrong.
When you're making games, whether it's the gameplay or the story which is your foundation, they need to tie into each other for it to be more than a game and an accompanying story or vice versa, a story with some accompanying gameplay.
Playing a game should be synonymous with experiencing a story. No matter what the story, no matter what the game. The best games are the ones who make the story integral to the gameplay, and make the experience of the gameplay integral to the story.
It doesn't need to be anything difficult, and even those moments when suddenly every input is bound to the same action carry the experience a lot. If you make it so that one of the two overshadow the other, then you've done something wrong.
Note that not every game needs to tell a story, but the ones that do benefit more from treating gameplay and story as one intertwined entity than two seperate subjects to be managed.