Stemmatology is an umbrella term for all scholarly and scientific studies focused on textual genealogy and the creation of a stemma codicum. It is usually concerned with reconstructing a specific stemma starting from the basis of the surviving witnesses, but may also deal with stemmata in a more abstract sense (hence this lexicon's name). The term is usually used as a synonym to stemmatics. As with many other fields, the endings -ology (from λόγος 'word, meaningful or scientific utterance') and -ic(s) (the adjective forming suffix -ικὴ, feminine because the feminine noun τέχνη 'art, field of study' is intended) tend to be used for the same purpose, namely to label a 'scientific field about X'.
If a difference between the two terms is perceived, stemmatology tends to be the wider term, whereas stemmatics may be confined to the Lachmannian method.
The Latin term 'stemmatologia' was already in use in the early 18th century, e.g. it appears in the title Stemmatologia Tigurina: Das ist Zürichisches Geschlechter Buch […] by Erhard Dürsteler (sine anno, but printed between 1706 and 1724). But the stemmata included in this book were people's genealogical trees and not yet representing manuscripts. The word stemmatographia was used synonymously (cf. J. Ramminger, stemmatographia, in ders., Neulateinische Wortliste. Ein Wörterbuch des Lateinischen von Petrarca bis 1700, URL: www.neulatein.de/words/1/001317.htm (used on 12.12.2014)).