The more lewd and horny fun way to say "Happy birthday", best to be used for people who are comfortable around lewd and horny or straight up enjoy it publicly.
Person 1: Hey I heard it's your birthday today?
Person 2: Yeah!
Person 1: Well Happy day of vaginal exit, hope you have a wonderful day
Person 2: What's that?
Person 1: Just a lewd and horny way to say happy birthday!