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A backtracking algorithm generates, explicitly or implicitly, a state-space tree.

Introduction to the design & analysis of algorithms / Anany Levitin

I wonder that whether the saying always holds. If yes, is it always binary tree? For any problem which can be solved by backtracking, skeleton of the solution can be generalized?

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Think about the chess problem or more simple 8-Queen problem are Tic Tac Toe game. The states are not binary trees. As seen from Quoara ;

A state space tree is a tree constructed from all of the possible states of the problem as nodes, connected via state transitions from some initial state as root to some terminal state as a leaf.

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