No, you don't have to order it on both devices.
When you buy a book, Amazon will (normally) automatically deliver it to your default device. Eg, if you buy a book on your Kindle, it will automatically be sent to that Kindle.
On any other device registered to the same Amazon account, the book will appear on the Archive page. The Archive lists all the books that you've bought, but which are not currently loaded on that particular device. By selecting the book in the Archive, it will download to the device.
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