Term for an A*-like pathfinding strategy where only the heuristic goal distance matters I am trying to find a proper term for the A*-like best-first pathfinding strategy where the node to expand next is the one with the least estimated distance from the goal, regardless of its distance from the source.

In best-first search algorithms, the node to expand next is the most promising one according to some evaluation function (which may take into account the current global knowledge).  In the normal A* algorithm, the evaluation function is the sum of the length of the currently know shortest path from the source and the heuristic estimate of the distance to the goal.  Is there a standard term for a similar strategy where the evaluation function is just the heuristic distance to the goal?

I was thinking about greedy and hill-climbing, but greedy in this context seems to be just a synonym of best-first, and in what is commonly referred to as hill-climbing, there seems to be either no backtracking, or just one-step backtracking, that is, old unexpanded nodes are discarded at each step.
This is greedy best-first search.