A dead center can come in a few different versions, each with a different name as well. A spur Center is the first to come to my mind. This is still a dead center for going in the head stock but it has the small "Wings" to help give it a little more bite in the block of wood.
Be careful when selecting a Live Center for turning pens. You want one that is hardened for turning metal not just a standard wood turning one. If you use a mandrel you want it to be a 60 degree center as well.
For turning pens you would use both a live and a dead center if you are interested in making pens with no bushings or are going to use the mandrelless bushings. This is also known as "Turning between centers" becasue your work is held between the dead center at the head stock and the live center at the tail stock. You can use a dead center at the tail stock but I do not recommend it. It is possible just like it is possible to catch catfish with your bare hands. It may be fun to try for a while but soon you will realize it also becomes a big mess.