Main series types with TCG orbs
Normal (Colorless)
Fire
Water
Electric (Lightning)
Grass
Fighting
Psychic
Dragon
Dark (Darkness)
Steel (Metal)
Fairy
Main series types without TCG orbs
Ice
Poison
Ground
Flying
Bug
Rock
Ghost
Secondary main series types
???
Shadow (Not actually a type but has similar properties to one)
Bird
Type orbs exclusive to the Trading Card Game
Rainbow - From a Special Energy card in the Team Rocket expansion
Miracle - From a Special Energy card in the Neo Destiny expansion
None - Used for moves that don't require energy cards to use since the Sun & Moon expansion
Aurora - From a Special Energy card in the Sword & Shield expansion
Unknown - Seen in the opening intro of the
Pokémon Card GB2: Here Comes Team GR! game
"Rainbow" - Used in the slot machine minigame in the
Pokémon Card GB2: Here Comes Team GR! game
But I can't take all the credit. The original sprite work was original created by a Pokémon fan site called Pokémon Factory. I loved it so much that I expanded on it (anything that isn't the 18 main types, Magic, Light, or Wind were created by me) and since the website hasn't been updated in years, I don't think they'll mind if I make use of it.
Here's the full set: The two versions they site had made, and my take on it.
Pokémon Factory version 1
Pokémon Factory version 2
My version
The 3 on the bottom are the site's new types:
Magic
Light
Wind