Swapping 2nd Gen Airpod Pro Charging Case Doesn't Work

Hello all,

I have a set of Airpod Pro 2s (model A2698) originating from a Lightning charging case. When I put this set of Airpods into a USB-C charging case for Airpod Pro 2s, they do not charge as normal and instead produce a "beep-boop"-esque sound with the exterior light flashing orange. Is this supposed to happen? I would believe that the two charging cases are the same aside from the different port.

Thanks.