About the differences - Plumeria Cuttings, Rooted Plants and Grafted Plants
Propagation by cuttings is typically the preferred method used by enthusiast and commercial growers because it is fast and easy. Cuttings will produce an exact reproduction of the donor plumeria. Some prefer a cutting to establish a root system by establishing it's own roots, while others prefer grafting cuttings (scions) to an already established root system called root-stock. When a cutting is grafted to the root stock it will not change the characteristics of the original cutting. One reason to grafting is to provide a better root system to the cutting than the donor plumeria.
A Plumeria Cutting is the typically the tip of a branch cut from a donor plumeria, usually about 10"-18" long depending on the donor plumeria growing habit. They can also be a center cut where there is no tip. Cuttings do not have roots. A plumeria cutting will eventually have to be rooted or grafted for it to survive.
Some helpful links: