Ringdoorbell 2nd generation adapter problem

Hi all. I am a new user of the ring doorbell 2nd generation and i am a bit confused. ( please forgive my poor English as i am a simple Dutch guy) The manual of the doorbell says that it can be hardwired trough a plug in adapter of 24V AC. So i went to the ring website to buy the correct plug in adapter for the doorbell. But the plug in adapter (cost €25) is 24V DC. The text states that this adapter is also for most other Ring doorbells like the doorbell pro. After a dissapointed call to the (don't) help center i still don't have a correct answer. Is this the right plug in adapter or did they made an error. It gets more strange if you look at the specs of the plug in adapter for the doorbell pro (cost€18). This one states that it is 24V AC and is only for the doorbell pro. I may be a simple man but this is confusing for everyone. Does anybody have an answer for me?