When I was younger, pans were lined with parchment paper. I used to work in the paper industry and can launch into a detailed discussion of how parchment is made, but I'll spare you, especially since there is a perfectly good explanation on Wikipedia.
While used for the same purpose, most baking paper used today is not true parchment. It's a silicone coated release paper. We call it a pan liner (not to be confused with a can liner, which is a garbage bag).
We buy them 1000 at a time and use them with just about everything we put in the oven, from bread to cake and cookies. Absolutely EVERY cake pan gets a custom cut liner EVERY time to prevent cake from sticking, even as we also use pan spray. Entirely too much labor goes into the cake-making process to risk damaging the cake after it is baked. They can also be used to make paper cones for piping (watch this video), although I prefer disposable plastic piping bags at the bakery.
We'll share our stash with you. Conveniently rolled in sets of ten full sheet sized (24x18) liners for $1 each.