Why I have a battery from the 2nd gen?

I want to change the batery of my kindle paperwhite 3 I bought in bestbuy because the batery stop working.

The problem is that the batery I have I think it is from the paperwhite 2... I dont know really.

my batery says S13-R1-D (supposedly 2 gen) and the guide for the 3rd gen says MC-354775-05

Which one I buy?