If you give the first twin a gift, he will attach two letters on one side and give it back to you.
If you give the second twin a gift, he will ignore it and show you his ID.
Despite being twins, these two are literally opposites.
Who are the twins?
One of the letters attached is not an English letter.
ID means "identity," not the literal letters "ID" as some answers have tried.
This is not wordplay, although the concept underlying this question has applications in linguistics (or so I'm told).
When you give someone a gift, they will always return a gift. Also, there is no distinction between gifts and giftees.