I use both a wooden peel and a metal peel, mainly for convenience. I usually dress the pizza on the wooden peel, using a bit of flour as a release agent, and remove the baked pizza from the oven using a metal peel, which is much thinner than the wooden peel and has a sharp edge at the tip that can easily slide under the pizza (whether on a screen or a pizza stone or tiles) to facilitate its removal from the oven. It is possible to use just a metal peel for both applications, but you have to be sure you put enough flour (or cornmeal, or semolina, or whatever) on the peel so that the unbaked dough doesn't stick to the peel. In my experience, this usually means lining up all the ingredients in advance and working fast when dressing the pizza.
A small metal peel can also be used for both applications for small, lightly-dressed pizzas like individual-sized Neapolitan style pizzas. They are often dressed on a well-floured marble or granite surface, placed onto the metal peel (by sliding the pizza onto the peel or sliding the peel under the pizza) and deposited into the oven. The same metal peel is used for removal of the finished pizza from the oven. Several videos linked on this site show these techniques.