once and for all, can someone explain why hardware wallets are different than paper wallet (and such)?

I don't own an HW wallet.

As far as i know, this type of wallet is a fancy way to keep the seed, while the actual crypto is always on chain.

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personally, i have three types of wallets – CEX (binance), active on-chain and dormant on-chain.

binance, well, nothing to explain. i just use it for transferring money into crypto.

active on chain – those are the wallets i keep on my phone/ wallet apps. those are used for casual transactions, trade, new investments, new losses, payments etc.

dormant on chain – well, those are wallets i opened a while ago, and removed from any device. i just have the seed/ private key written on paper that i store hidden from sight (clue – not here). sometime, in the far or near future, if i ever need cash, i will just enter those account and drain them.

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is there a real difference between actual HW wallet and my dormant one?

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EDIT – there are good answers here, but most of the comments enhance the misconceptions about HWW, even within the crypto community.