In ordinary writing we use the terms interchangeably. But there is actually a difference.
This is a labyrinth. Visitors enter by a single entrance and follow the winding pathway until they arrive at a single exit point. Some people enjoy "losing themselves" in the pleasant walk through a labyrinth.
This is a maze. It may have several entrance or exit points and has dead ends. Mazes usually have lookout towers, so visitors can see the next steps in a maze. It is a real test of memory and problem solving.
images from wikipedia
On a mathematical note: our own Brian J Skinner PhD and expert in all things math reminds me:
"you can make an easily-solvable "labyrinth" out of any maze just by keeping one hand against the wall at all
times and following wherever it takes you. Eventually it will take you out the exit."
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