Birthdays

Birthday cake, wrapped gift, balloon, and party popper cover the core visual elements of a birthday message or post, and are among the most universally recognized celebration emoji.

New Year and general celebrations

Confetti ball, sparkles, and clinking glasses are commonly used for New Year's messages as well as general milestone celebrations, since they aren't tied to any single specific holiday.

Seasonal holidays

A Christmas tree, jack-o-lantern, and fireworks each signal a specific holiday quickly — winter holidays, Halloween, and Independence Day or similar firework-based celebrations, respectively.

Weddings and graduations

Covered in more depth in a dedicated wedding emoji guide, but graduation cap and diploma-style emoji specifically fill the gap for academic milestone posts that birthday or general party emoji don't quite capture.