In Sutton & Barto's Reinforcement Learning: An Introduction, page 54, the authors define the terminal state as following:
Each episode ends in a special state called the terminal state
But the authors also say:
the episodes can all be considered to end in the same terminal state, with different rewards for the different outcomes. Tasks with episodes of this kind are called episodic tasks.
I believe there is also a fundamental difference between a terminal state, nonterminal states and plain, normal states:
In episodic tasks we sometimes need to distinguish the set of all nonterminal states, denoted S, from the set of all states plus the terminal state, denoted S+.
In the first quote, it appears as if the terminal state is just a term to describe the final state of an episode, but, from the second quote, I understand that the terminal state is the same no matter the outcome of the episode. If we consider the game of chess, what would we consider as a terminal state? Would it be the state that, if reached, will end the game (checkmate), no matter the result (win, loss)? But then how can we describe a state that would lead to draw? If we say about a state that leads to a draw that it's a nonterminal state since we can play an "infinite" number of turns without reaching a win or a loss hence without reaching the terminal state, aren't we implicitly supposing that reaching a draw isn't a result for which we should attribute a reward (e.g. 0)? And if we name a state that leads to a draw a terminal state, then what would be the difference between a normal state and a nonterminal state?