The two words are used synonymously but they actually mean something different. A labyrinth is a maze where all you have to do is walk and keep walking and you will reach the centre:
As long as you simply follow the path, you will reach the centre.
A maze on the other hand has false trails, dead ends and sometimes pitfalls. You have to explore all the turnings, even when many are ones that turn you back on yourself:
You can get totally lost in a maze: people have to be rescued from the famous one at Hampton Court. A labyrinth is different: you just keep going and follow the path ahead.
But if you get to the centre eventually, does it make a difference how long it took, or how short a time?
Is it the journey that is important or the destination?
Which is your life: maze or labyrinth?