In the literature on mazes, the distinction you are talking about is described to using the terms "simply connected" abd "multiply connected" from topology. Se

In the literature on mazes, the distinction you are talking about is described to using the terms "simply connected" abd "multiply connected" from topology. See e.g. https://www.britannica.com/topic/number-game/Mazes https://www.britannica.com/topic/number-game/Mazes