I've disassembled the die and the decapping pin looks like the one on the right in your photo. I can't explain why this "pistol" like pin would have been sent with the .223 full length sizer die.
If it has a straight sided decapping pin, it might be a neck sizing die, not a full length sizing die.
My Lee FL sizing die has 223-DO stamped into the side of it. The neck sizer has nothing stamped on it that I could see. Here is a link to Lee's Deluxe Rifle Die Set. The FL sizing die is on the far left, the neck sizing die is on the far right.