Elemental magic is three common magic in Final Fantasy series including fire, blizzard, and thunder. The big different in FFXV is that it comes in a form of crafted item.
In order to craft an elemental magic, a player needs to gather elemental energies (fire, ice, and thunder), combines them together, and puts it into a magic flask. Spell damage depends on the number of energy used while crafting.
In addition, consumable items can be used as a crafting material creating additional effects to that elemental magic including a healing cast, dual cast, and even a poison cast.
Elemental magic does not cost any MP but has a slight cooldown after usage. It also has various effects based on weather and environment condition. Casting fire on a dry glass can leave that area burned for a while. Blizzard can freeze an enemy. Using thunder on a raining day increases its damage output.
It is not necessary to save a magic flask in only a difficult fight. Since magic can deal great damage to a group of monsters at once, it is an ideal for leveling.
Ring magic is only available to the wielder of the Ring of Lucii. It is a royal accessory passed down from King Regis to Noctis. The wielder can cast several powerful non-elemental magic such as the death spell.
Other spells from the ring magic have not been revealed yet. They are expected to be other famous FF spells such as ultima, demi, meteor, and even support magic like protect, reflect, haste, and so on.