Telegram is completely cloud based. So all your conversations, except secret chats that are end-to-end encrypted, are stored on Telegram servers in plain text for as long as your account is active. This is why you can get a new device, activate it for your account and get all your conversations back on it from the Telegram servers.

Wire and Signal work differently. They use their servers as a temporary storage to hold your messages until the recipient comes online and then deliver them. Wire also retains the messages for a few days to allow delivery to multiple devices that a user may be using, with each device possibly coming online at different times. Signal doesn't have to support this because it's tied only to a single device, which is your phone.