In Pokémon X and Y, the player can receive the Shiny Charm from Professor Sycamore after obtaining all the Pokémon in the National Pokédex, with the exception of event Pokémon.
You have to complete the National Dex in order to recieve it, that means all the Pokemon, with the exception of event Pokemon.
That means you must have caught every Pokemon, not just seen it. Same for the crown, in order to get the crown you must have caught all of those Pokemon, not just seen them.
Sources: Bulbapedia, the links above and knowledge
Hope I helped.