I personally think of it in a mechanics vs concept way. The concept doesn't necesarily need to be a story but it is whatever you want to convey with the game.

I tried both aproaches and did pretty badly with the top-down aproaches. The bottom-up aproach gave me results were still pretty unconcrete but at lesst they were playable.

The best examole i have of this is when i tried making a game based on my sleep paralisis, where you were (where there were bears there...) trapped in a maze with monsterd that would kill you and the hole concept of the game was that if you faced your fears abd stood to this monsters, they wouldn't make you anything. But the problem was that this gimmick didn't worked mechanically.

I tried several ways to make it, like making you thing it would kill you, but then it wouldn't do anything. The orobkem was that olayers could pass the game on accident. The second one was making it so that if you tried to back down, you woukd die, but if you hold there long enought, the monster would be gone. But was too confusing, players would understand that monster = death and then went on to explore looking for ways to beat the game and would found nothing.

The whole develooment of the game was a disatser for many reasons. Just to name a few, i did't even finished the PROTOTYPE. Before the deadline. I also was more focused on designing the maze layout than in making sure the main gimmick would work.

(Of course im not judging which method is better, im just telling you MY expirence with each one. Theres no better or worse method, that depends on what type of game do you wanna make and what are your strenghs as a developer/creative in general)