The decorative piece that attaches to the end of a curtain rod or drapery pole is called a finial. Typically, they are the drapery hardware component that first attracts your attention when deciding which style or collection you want for your curtains. There's really no limit to the different styles, shapes, colors and sizes available. An end cap is a type of finial that is usually small and understand and is frequently used on the back rod of a double treatment, or when you lack the required wall space for a larger finial.
Finials attach to their corresponding curtain rod in several different ways. Most finials have a screw embedded into their base which allows you to easily mount it into the pre-drilled hole in your wood rod or a finial adapter frequently used with metal or wrought iron rods. Sometimes, finials attach using a set screw. This method is typically reserved for metal drapery rods. Like all drapery hardware componets, it's very important that you don't try to mix-and-match pieces from different collections. Always use the drapery rod or pole from the same brand and collection as your finial. If you don't, there's a good chance the finial isn't going to fit.
Nearly all finials for wood style drapery hardware are made from resin simply because true hand-carved wood pieces would be extremely expensive to produce. Resin finials look great and are very durable. Many collections offer coordinating accessories like holdbacks and brackets that match popular finial designs as well. And, by using wall adapters and posts, you can use any finial as a tie back to create your own style window treatment.