Vitalik Buterin refers in his blog to "State Tree Pruning".
Gavin Wood more recently talks about the "State Trie Pruning".
So, what is it, the the State-Trie or the State-Tree?
Tree is the more general term; trie is a more precise term technically since it's a more specific type of tree... Trie is more nitpicky. I think using the general term, "tree", is better for tagging purposes and is accurate enough.