Node

A node is a vertex in a game tree, and are often categorized based on a number of properties.

Game Tree Topology

The Root node is the node at the start state of the search.
Leaf nodes are nodes which are not explored, but which instead have a value immediately returned, such as at terminal nodes or when reaching depth 0 in a depth-limited search.
Terminal nodes are a kind of leaf node which is an end state of the game, such as when a player is in checkmate or when the fifty-move rule is triggered.
Interior nodes are nodes which are not leaf nodes. These nodes are explored further by the search.
Sibling nodes are nodes which share the same parent node.

These terms relate to depth-limited searches.

Horizon nodes are leaf nodes with depth 0, and so are leaf nodes (in the absence of ).
Frontier nodes are interior nodes searched with depth 1.
Pre-Frontier nodes are interior nodes searched with depth 2.
Quiescent nodes are nodes with depth at or below 0 which are searched as part of quiescence-search.

These terms relate to alpha-beta search frameworks.

PV nodes (sometimes referred to as Type 1) are interior nodes where a move is found with a value that exceeds alpha but not beta. In pvs, this refers to any node searched with a nonempty window.
Cut nodes (sometimes referred to as Type 2) are interior nodes where a move is found with a value that exceeds beta.
All nodes (sometimes referred to as Type 3) are interior nodes where no move is found with a value that exceeds alpha.