It was once thought that Diancie was an evolved form of Carbink, but that was discovered to not be the case. Instead they are actually two different Pokémon. However, that doesn't mean they don't have a connection to each other. They actually have a lot more in common than you'd think which would explain the mix up. Here are some things I have noticed.
What is Carbink you might ask? Carbink is this adorable little guy you see on the left. Isn't it cute? Like Diancie, Carbink is a Rock/Fairy-type and is classified as the Jewel Pokémon. Both are listed as genderless and share a lot of physical resemblances. It's no surprise people thought Diancie was an evolution of Carbink. But why so many things in common then? The reason stems from the fact that Diancie is actually a mutation of Carbink, hence the similarities. While I have no idea what the cause of the mutation would be I'd imagine it is an exceedingly rare occurrence considering how Diancie is called a Mythical Pokémon––nevermind the fact that Nintendo decided to make this Pokémon unobtainable through normal gameplay.
But that's not all there is, is it? Nope! Turns out Carbink and Diancie share a near identical moveset. While the majority of their moves are learned at the same levels, there are certain exceptions. These exceptions are Carbink learns Power Gem where Diancie learns Trick Room and only Diancie learns the move Diamond Storm. They also share a lot of the same base stats as well including Health, Defense, Special Defense, and Speed. The only difference is Diancie's Attack and Special Attack are higher than Carbink's. Other than that that's all I've been able to find in common between these two. Cool though, isn't it? I definitely think so!