Hi!
The main difference from having it stored “in Daedalus” is that paper-wallets are “cold” meaning that your secret keys are not stored on a computer, which means there’s no internet access to it.
When you “keep you ADA in Daedalus” (meaning - you have your wallet restored and available in Daedalus) - then your secret keys to this wallet are stored on the computer. If you have a spending password - then you keys are encrypted, but still stored on the computer. A little time ago there was some discussions on this forum and in telegram groups about how hackers can potentially steal Daedalus files, acquiring access your secret keys, and this is exactly why it is important to have a spending key to all Daedalus wallets. And the safer those passwords are - the harder it will be for hackers to get access to actual keys.
When people don’t want to have constant access to their wallet, but maybe only have it as a store of value and as an address where to send coins - they don’t want to risk having their keys constantly on their computer. And there’s a way how people solved this - you just create your wallet, write down your secret words, store your receiving address somewhere and delete this wallet from Daedalus. This way you have a completely cold wallet - there’s an address where you can deposit coins, and there’s secret key that you can use anytime to get back access to spending those coins on this address.
The paper-wallet is just a bit more official and a bit more secure way to do the second option 
The way paper-wallets are generated - your secret words are never shows on the screen in their entirety and they never once stored on the hard-drive, and there’s never even a wallet as is in the Daedalus, until you decide to restore it from its paper form.