Both Whatsapp and Telegram (and many other messaging apps, browsers, and operating systems) use the Emoji suite.
Different types of Emoji are the result of different fonts for emoticons; they have a different appearance depending on the font used, but the base is always a set of Unicode characters.
Both Whatsapp and Telegram use the Apple implementation, apparently, as the Ivo link points out. Also see this github for more licensing information.
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