How can I remember which data structures are used by DFS and BFS?

Draw a small graph on a piece of paper and think about the order in which nodes are processed in each implementation. How does the order in which you encounter the nodes and the order in which you process the nodes differ between the searches?

One of them uses a stack (depth-first) and the other uses a queue (breadth-first) (for non-recursive implementations, at least).

Queue can be generally thought as horizontal in structure i.e, breadth/width can be attributed to it - BFS, whereas

Stack is visualized as a vertical structure and hence has depth - DFS.