I am on a two-dimensional grid-maze where you can only move horizontally and vertically. The edge cost is 1 and I use the Manhattan distance to estimate the distance from a node to the target.
My question is whether or not it does make a difference if you start in your current node finding the way to your target or starting on the target node and finding your way back to your current node?
No it doesn't make any difference whether you work forward or backward. Keep in mind though that in practical applications, you often have many goal nodes but almost always a single start node. If you only want to reach one goal node, it's better to search forward from the start node.
Also, note that A* will yield the optimal solution if using an admissible heuristic. There might be multiple solutions that are equally optimal, so searching backward rather than forward could lead you to a different, but just as good, solution.