https://store.extension.iastate.edu/Product/Growing-Garden-Peonies-PDF. here is an article which should answer most of your questions.  Your peony sounds like it is herbaceous.. dying back to the ground each year to revive in spring. There are two other types. One is a tree peony which has a permanent above ground structure. The other is a cross between the herbaceous and the tree peony and is called an Itoh. 
If this article does not fit the bill, please get back to us. If you search for more information online add “extension” or “edu” to your word search for reliable university based resources.