I believe letterboxing is slightly different or at least it's supposed to be. The original idea of letterboxing was to find a container and post your calling card.
With non-virtual geo caches the idea if to find a tupperware box (or old army ammo box or similar) full of tat, take one piece of said tat and leave a piece a piece yourself for someone else to take. There is also a book there to say when you found the cache, what you took and what you left. Some items are marked so that people take them to another cache and report on a web site where they took it. Folks then like to watch their item move around the world.
Now many call leaving a plastic box full of tat in the countryside geo caching. Many call it littering.