誕 birthday / birth

That baby was born with a sunTAN.

He said he wants to prolong his birthday so he gets presents forever.

birthday ★★★★☆ FP
誕生 (birth) + 日 (sun, day) = 誕生日 (birthday)

birthday

If you want to say Happy Birthday, you'd just say 良い誕生日！　（よいたんじょうび！）.

However, if you're asking someone what day is their birthday, you'd add 'の日’　like this:
誕生日の日はイツ？　（たんじょうびのひはいつ？）

birth ★☆☆☆☆
誕 (birthday / birth) + 生 (life / birth) = 誕生 (birth)

the birth of (figurative) (i.e. Miles Davis' "birth of the cool" album)