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?
Hint #1:
One of the letters attached is not an English letter.
Hint #2:
ID means "identity," not the literal letters "ID" as some answers have tried.
Hint #3:
This is not wordplay, although the concept underlying this question has applications in linguistics (or so I'm told).
Hint #4:
When you give someone a gift, they will always return a gift. Also, there is no distinction between gifts and giftees.