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So like
With a paper wallet, the piece of paper and the string of characters is **all there is**. Sure, it’s a key, but you can’t really use it. You can’t show the paper to a merchant to send money, you can’t generate a new address, etc.
To do anything useful with a paper wallet at all, you need to copy it over to some sort of computer. At which point it becomes, however briefly, a software hot wallet.
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On the other hand, with a hardware wallet, the paper is your **backup**. You can simply not have it, if you like to live dangerously. Or you can store it on an external drive, like backups of your vacation photos — except with your vacation photos, you won’t lose all your money if a hacker steals them. Which is why you (a) should make backup and (b) should keep it off computers.
With the paper out of the way, the hardware wallet can do everything your software wallet can. It does not need the paper to operate, and it also can’t really be hacked the way a software wallet can.