Depth-first search (DFS) explores a tree by going as deep as possible along a branch before backtracking. In binary trees, DFS gives rise to the classic traversal orderspre-order,in-order, andpost-order, each defined by when you "visit" the node relative to its left and right subtrees. Pre-order visits the node first, then left subtree, then right subtree. In-order visits left subtree, then the node, then right subtree. Post-order visits left subtree, then right subtree, then the node. These are all DFS-based because they fully explore subtrees before moving sideways to another branch.
Level-order traversalis different: it visits nodes layer by layer from the root outward (all nodes at depth 0, then depth 1, then depth 2, etc.). This is a hallmark ofbreadth-first search (BFS), not DFS. Textbooks emphasize this distinction because DFS and BFS have different properties: BFS naturally finds shortest paths in unweighted graphs and produces level-order traversal in trees, while DFS is useful for tasks like topological sorting, cycle detection, and exploring structure recursively.
Therefore, the traversal order that is impossible to produce as a depth-first traversal of a binary tree is level-order traversal. The DFS orders (pre-, in-, post-) are all achievable by depth-first strategies, typically implemented recursively or with an explicit stack.