What's the difference between "mythical" and "legendary" Pokémon?
In short, Mythical Pokémon are a subset of Legendary Pokémon.
A Legendary Pokémon is characterized by its rarity, its inability to spawn offspring of its own evolutionary chain, and its presence in the lore. Usually, only a single Legendary Pokémon of its species exist in a game, and it is encountered by interacting with it outside of battle or by other special means. Some examples of Legendary Pokémon are Articuno, Raikou, Heatran, Mewtwo, Thundurus, and Zygarde.
A Mythical Pokémon is a Legendary Pokémon whose main method of acquisition is out-of-game, real world distributions such as online events or codes given at specific stores. Mythical Pokémon cannot be encountered by just playing through a game. Some examples of Mythical Pokémon are Mew, Victini, Jirachi, Arceus, and Volcanion.
In addition to DanmakuGrazer's answer, there are some other named groups of pokémon to be aware of, although both have unofficial names:
Sub-legendary
This group is for pokémon who are usually encountered in ways similarly to regular legendaries (one per game, usually encountered in the overworld, story talks about their rarity) but they aren't nearly as powerful as other legendaries. This group mostly comprises pokémon who have a Base Stat Total (BST) of 600 or below, and can't be bred.
A key feature of this group is that all of its pokémon are allowed in places where other more powerful legendaries are banned, such as online PvP battles or in-game facilities like the Battle Tree. All pokémon in this group have a green background in the Gen 7 pokédex.
The pokémon in this group are: Articuno, Zapdos, Moltres, Raikou, Entei, Suicune, Regirock, Regice, Registeel, Latias, Latios, Uxie, Mesprit, Azelf, Heatran, Regigigas, Cresselia, Cobalion, Terrakion, Virizion, Tornadus, Thundurus, Landorus, Type: Null, Silvally, Tapu Koko, Tapu Lele, Tapu Bulu, Tapu Fini, and all Ultra Beasts.
Pseudo-legendary
These pokémon have a similar BST to sub-legendaries, but are otherwise normal pokémon. All pseudo-legendaries can breed, evolve twice, and their final evolutions have a BST of 600.
The pokémon in this group are: Dragonite, Tyranitar, Salamence, Metagross, Garchomp, Hydreigon, Goodra, Kommo-o, Dragapult, and all of their evolutionary families.