Only the encryption layer of the protocol is the same, they are not really compatible otherwise.
I assume it's a design trade-off when you have E2EE and don't store any messages on the server. With Signal (and I assume Wire) you have to register each device and each device needs to manage its keys. Every message is send multiple times, once for each device, and each device has an independent message queue on the server. That's why you only get the messages from after you registered the device.
Whatsapp doesn't have to do any of that and can just keep the keys on one device.
I assume it's a design trade-off when you have E2EE and don't store any messages on the server. With Signal (and I assume Wire) you have to register each device and each device needs to manage its keys. Every message is send multiple times, once for each device, and each device has an independent message queue on the server. That's why you only get the messages from after you registered the device.
Whatsapp doesn't have to do any of that and can just keep the keys on one device.