Comment 11 for bug 1779569

Web browsers have their own system for rendering text and therefore color emoji. Firefox currently uses a version of EmojiOne but is switching to the Twitter emoji set. See https://bugzilla.mozilla.org/1358240

Honestly, the bug report you filed is too broad and in some cases is already duplicated by existing bugs.

For reference, you might find this page interesting (it's a large page):
https://unicode.org/emoji/charts/full-emoji-list.html

Ubuntu 18.04 LTS installs the Google emoji font by default and that page does actually display correctly for me with Firefox. Web pages can specify a particular color emoji font though. Therefore, you will see different emoji sets on different web pages and that's not really a bug.