Glossary of Terms
High Fantasy: Many distinct fantastic elements, often impossible or implausible. These elements tend to be widespread and create significantly different cultural and technological norms as a result of their existence. Many or at least some of these elements impact the day-to-day lives of most citizens and lifestyles have adapted accordingly. Beware of lightning trains conveying the middle classes at speed across the country. Magic or its equivalent is routinely employed in war both defensively and offensively and even bandit camps might have precautions to at least defend against attacks by wizards. Things which would seem powerful to the low-fantasy world such as magical healing are commonly available to those who can afford it, whilst even feats such as raising the dead are not unheard of (though likely still strongly limited by resources or power requirements). The Dungeons and Dragons standard setting is a good example of a High-Fantasy world.
Medium Fantasy: Distinct fantastic elements, some of which may be physically impossible on Earth (flying horses, everflowing goblets of wine). Cultural and technological norms may be quite different from Earth-equivalent societies either as a consequence of these elements or as a deliberate design feature of the setting creator. Most of these fantastic elements may not impact the day-to-day lives of most citizens, but powerful or wealthy classes might have comparatively common access to them or have their lives affected by them. Soldiers (especially noble soldiers) might have access to expensive facilities in the form of potions or holy altars to cure wounds sustained in battle. Powerful noble families might have access to magic weapons and armies even if they do not employ wizards are likely to have developed tactics to combat them. Court sages would likely be experienced in fantastic lore, at least to the level of knowing some details. A device capable of raising the dead would still be a very powerful, even legendary thing. David Drake's "Lord of the Isles" series is a medium fantasy during the millenial peak of magical power. The Harry Potter series would qualify as Medium Fantasy.
Low Fantasy: Close to whatever technological and cultural norms would be in the Earth-equivalent society you are using as a base, or else a new society/setting with relatively few fantastic elements. Fantastic abilities tend to be on the upper level of what is physically possible (e.g. breeds of horses that can travel at a sustained gallop for a full day, or half again as fast as a normal racehorse, but not horses that can gallop over thin air). The fantastic elements that do exist may not impact the lives of most citizens in the setting as anything more than fairy tales, or only as a distant impact in the same way that the King might be. In such a setting a chalice that heals wounds and cures disease when drunk from is a big thing, on the level of the Grail in our world. The king might have access to a powerful vizier who can obtain fantastic creatures or artefacts, but most would never see them. The legend of King Arthur and the Knights of the Round Table is an example of low fantasy.
Ultra-Low Fantasy: The story is set on Earth, or close to it as possible. Everything present could be found on Earth.
High Magic: Magic is common, powerful and probably replaces investment in technology. Beware lightning trains. Even if magic is still restricted to a lucky few, those few are very powerful indeed and capable of literally earth-shattering acts. Magic is regularly employed in war, crafts and sciences. Some may pursue magic as a sole ability whilst others employ it to augment their other skills, e.g. shipwrights who employ telekinetics to build ships faster or potions to improve the buoyancy of their vessels.
Medium Magic: Magic is uncommon, but comparable or superior to local technology in its power. It may be well known, or cloistered within secretive guilds and covens. Magic or magical effects may still not affect the average person except in broad ways ("Don't go to Brook's Field, nothing grows there since the Stone Burning") but those who venture beyond society's norms or those in positions of power might have reason to come into contact with it. If magic is comparatively widespread, those in a position to be affected by it on at least a semi-regular basis will have developed tactics to employ or account for it.
Low Magic: Magic is rare, known only to a few and probably quite weak. Spells to locate or divine, or that have minimal impact upon the physical world, are more likely to be present. The effects of magic may be subtle to the point where it is uncertain if magic is even happening at all. Mages in this setting (depending on cultural norms) might be witch doctors, alchemists or witches, all with about as much clout and observable effect as they had in our world. Magic does not generally affect the lives of most people except in myth and legend.
No Magic: There is no magic. If there are magical-seeming effects, they are either technology or Sufficiently-Advanced Aliens. Note that any of the above Magic classes can also be a result of Sufficiently-Advanced Aliens.