This article is a nice exploration of an approach called Graph Search, which essentially trades compute for memory by doing extra compute work (hashing the game states) to check to see if the nodes are already visited. That saves us from re-recording nodes we already saw, and consequently converts trees (free of cycles) into directed acyclic graphs.
This forces some tinkering with the tree search to get correct results, specifically it demands a focus more on edges (actions or moves) as the unit of optimization, rather than on vertices (states). It’s a well written technical essay in literate programming written by someone who understands their subject.
Applying the algorithm adds a hash associated with each node, and a counter on each edge. On the other side you're de-duplicating identical states in your search space, saving the memory of duplicate nodes but more importantly saving compute by not requiring independent searches of the same state space. Whether this trade off actually saves memory will be determined based on how likely duplicate states are in your search space.
Otherwise your summary is absolutely spot on.