Enchantment type

An enchantment type is any subtype used for the further classification of enchantment cards.

Other then creature types enchantment types don't have to appear on all enchantments. Instead they are only introduced for mechanical purposes.

Rules
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Aura
Enchantments that possess the rules text "Enchant" are of the Aura subtype. These enchantments must be attached to an object specified by the Enchant ability, and exert an effect on that object.

An Aura's text box will specify what kind of permanents it can be attached to, reading "Enchant [type]." When an Aura spell is played, it must target an appropriate permanent, and when it resolves, it comes into play attached to (and no longer targeting) that permanent. If the permanent it is attached to leaves play at any time, becomes a type that the Aura cannot enchant, or gains protection against any of the Aura's characteristics, the Aura becomes unattached and will go to the graveyard.

Auras can be destroyed by cards with "destroy target aura" or "destroy target enchantment" as auras are just subtypes of enchantments.

Aura subtypes have no mechanical baggage, and tend to merely be markers for other cards to refer to.

Cartouche
Cartouches are Auras that enchant creatures, giving them a boost that represents some kind of success or accomplishment. They give the creature they are enchanted to a boost of +1/+1 and a keyword, which is primary in that color. They also carry a secondary enter the battlefield effect, which also directly reflects the flavor of its color. Cartouches return their owner's Trials to their hand when they enter the battlefield.

Curse
Curses are Auras that enchant players. They were introduced in Innistrad and featured in the Innistrad block and Commander 2013. Although all Curses enchant players, not all enchantments with the "Enchant player" rules text are Curses. In fact, the ability has been featured on cards from previous expansion sets, such as Psychic Possession from Dissension.

Rune
Runes are Auras that can enchant any permanent, though as of now only provide an effect if attached to a creature or an equipment. All of them draw a card upon entry, and bestow a keyword onto either the creature or the equipment's holder. Both cards that refer to Runes can search for them from the graveyard or library.

Saga
Sagas are enchantments with several triggered effects that change with the passage of turns as each "chapter" unfolds. As the Saga enters the battlefield and then right after the player's draw step, they add a lore counter to the Saga, triggering the correspondent chapter ability, until the third chapter is reached and the Saga is sacrificed. Flavor-wise, each Saga is meant to tell the story of a key event from the past, like the rise of Benalia or the Mending.

Shrine
Shrines are enchantments that possess an ability that is triggered at the beginning of its controller's upkeep. The effect is proportional to the number of Shrines that player controls. Shrines were introduced in Champions of Kamigawa, and all Shrines possess the legendary supertype.

Shard
Shards are an enchantment with ", Sacrifice this enchantment: Scry 1, then draw a card."