I was always under the impression that a Maze and a Labyrinth were two different things. The purpose of a labyrinth is to find the centre where as the purpose of a maze is to find the exit. Is that correct?
I agree there are those two different sorts, but not with the strict separation of the definitions of the two words, maze and labyrinth.
The Labyrinth was the maze that the minotaur lived in. It is generally understood to have been a "puzzle maze" in which it was possible to get lost. That is why Theseus needed to use a string to find his way back out after killing the minotaur.
"Labyrinth" is believed to derive from a word for a double bitted axe, and possibly linked to the fact that the double bitted axe was a motif associated with goddesses, rather than gods. I looked it up because I had always vaguely (and incorrectly) connected the "laby..." sound with "labor" (work) as in "laborious".
Coins were later struck with a representation of a unicursal maze (single path, not a puzzle) which was intended to represent the original Labyrinth. Already, in ancient times, there was some confusion over the distinction between the single-path maze and the multi-path puzzle maze, and which one should be termed a "labyrinth".
"Maze" comes from the same root as "amaze" and implies that it is something that "drives you crazy": a frustrating puzzle.
However, in common usage, the two words can be used to refer to either sort: the single route or the puzzle maze. Therefore, when the distinction is important, it is usual to refer to a "unicursal maze" or a "puzzle maze".
"Labyrinth" tends to be used less often when describing actual mazes (very few people refer to Hampton Court Labyrinth rather than Hampton Court Maze) and is more often used figuratively: "He lived in a labyrinthine manor house..."
A unicursal maze has a single route through it. In effect, it is a path with many twists and turns but no forks or junctions. There is no reason why a unicursal maze could not be designed with an entrance and an exit, but nearly all of the traditional and "ritual" ones have a path that leads to the centre. There's one way in, and the reverse route to exit, assuming that you don't cheat. (In my experience, all of the unicursal mazes I have seen have had no hedges, walls or fences, so there is a theoretical possibility of just taking a short cut, but only a cad and a bounder would do so.)
Puzzle mazes have forks and junctions, and it is possible to get lost in such a maze. A puzzle maze could be designed with several possible "solutions" but most of them have only one. In my experience of puzzle mazes that I have visited, all or most have a central objective. You go in through the entrance, wander about a bit, find the middle, where there is often a bench or statue or other feature, then you find your way back out.
Therefore, both kinds (unicursal and puzzle) are commonly designed for you to find the centre, although either sort could be designed for you to get from the entrance to the exit, with no central point.
The "standard" 7 ring unicursal maze, which is a common motif, is made of 7 concentric loops and the overall shape is roughly circular. However, more elaborate examples have lobes (e.g. the one at Saffron Walden) and there may be many more than 7 rings, although there is still only one route.
There is an important distinction between two sorts of puzzle maze. If all the sections of hedge are in contact with each other, then it is simple to find the centre (or exit): all you need to do is trail your fingers along one wall and keep walking. You may have to walk a long way and down and back along several blind alleys, but you will always "solve" the maze. However, if the maze is designed differently, then some parts of the hedge will not be in contact with the others. Therefore, if the solution to the maze involves passing through one of these, you cannot solve the maze simply by following one wall.