Emojis are actually a part of codified Unicode standard that evolves over time and pretty much every typeface that is able to show emoji is able to show the same amount of them, unless they're working on outdated specifications, then you get the infamous white square that's used for unsupported characters. The difference between how emojis look between different devices (iOS, Android, Microsoft etc.) is because of the system font that's used by the OS when it sees emoji (for iOS / MacOS for example it always falls back to Apple Color Emoji font).
Stickers on the other hand are things that are added by third party applications like Facebook Messenger or iMessage and are not limited by a standard, allowing them to be much more custom and expanding much quicker. Since they're not standardized though, they rarely work cross platform, while emoji are universal.