If Wikipedia is any guide: Low Fantasy
Low fantasy or intrusion fantasy is a type of fantasy fiction. It has been defined as fiction where magical events intrude on an otherwise normal world. It thus contrasts with high fantasy stories, which take place in a fictional world with its own set of rules and physical laws.
High Fantasy was a term coined by Lloyd Alexander in 1971. It means a fictional story that takes place in an entirely different, alternate or secondary world.
High Fantasy is also known as Epic Fantasy
There isn't a "medium" fantasy but there are other genres:
- Heroic Fantasy
- Sword and Sorcery
- Medieval Fantasy
- Historical Fantasy
- Hard Fantasy
You can read about them and more in Wikipedia... List of Genres