Is there any difference between the following two sentences?
1 What do you want for your birthday?
2 What do you want on your birthday?
My guess is that #1 is asking about a birthday present and #2 means anything you want on the very day of the person's birthday, not necessarilly a birthday present. The answer for Question 2 could be "I want some paper plates for my birthday party (held on my birthday). Could you bring some for me?"
(1) is what family and friends might ask, meaning, what present do you want me to give you for your birthday.
(2) 'on your birthday' is used differently.
You should shop at Smith's Bakery because on your birthday each year they give you a chocolate cake for free.
The Battle of Hastings falls on my birthday.
If someone wishes to ask, do you want a party at home, or to go out to dinner on your birthday, they would ask: "What would you like to do for your birthday?"