Why do depth-limited search algorithm and BFS have different memory complexity?
Let be b the branching factor of the tree.
Let be d the depth of the shallowest solution.
Let be l the limit given to depth-limited search algorithm

Breadth-first search (BFS)
In the worst case, suppose that our solution is at depth d, and we expand all nodes but the last node at level d, then the total number of generated nodes is $ O(b^{d}) $.
As all these nodes must retain in memory while we expand our search, then the space complexity is $O(b^{d})$.
Depth-limited search algorithm
Unlike BFS, Depth-limited search algorithm has a very modest memory requirements, it needs to store only the path from the root to the leaf node, beside the siblings of each node on the path. Depth-limited search algorithm removes a node from memory once all of its descendants have been expanded.
DFS requires storage of only $O(bl)$ nodes thus space complexity is $O(bl)$.