How is a trade secret different from a patent?

One of the fundamental elements of patent law is that, in exchange for being able to protect his invention, the inventor must publicly disclose the details of his invention. The whole purpose of trade secret law, however, is to protect one’s inventions when the do not publicly disclose it. In fact, if something is publicly disclosed, it is no longer entitled to trade secret protection. Thus, patents and trade secrets are pretty much the opposite of each other, and you can not have both patent rights and trade secret rights in the same thing.

Patent protection is stronger than trade secret protection - nobody can make or use your patented invention regardless of whether or not they know about your invention, but if they make or design the thing you are protecting by trade secret without actually using your trade secret, they are free to use it and you cannot stop them. However, the protection offered by trade secret law can theoretically last forever, while the protection offered by a patent only lasts for a limited time. This leads to the obvious question of whether you should keep something a trade secret or patent it.