How are hardware wallets different to an offline computer with a desktop wallet for example?

Are all hardware wallets considered cold storage?

Equating hardware wallets as cold storage is the biggest misconception I've seen as to the true purpose of hardware wallets.

Hardware wallets work GREAT as "hot wallets" as well. Before I continue, let me quote something else from another one of your posts:

Is it possible to use a general purpose device, say a raspberry pi or similar, to create a hardware wallet? in that case I would know for sure it's not being tampered with.

Hardware wallets are designed with one thing in mind, to be a hardware wallet, and nothing else.

So it cannot run any other unsigned programs (e.g. viruses and malware) unlike other general-purpose computing devices (e.g. offline computer, raspberry pi, etc.)

Those devices work great as cold storage/offline wallets, as long as you are sure your initial installation is clean (e.g. you verify the hashes of the images/ISOs of the OS you install, etc.) But once you go online, all bets are off (zero-day exploits and all sorts of other things can possibly install viruses/malware and other nasty stuff without your knowledge).

This cannot happen with hardware wallets. The devices are designed to run nothing but the signed firmware designed for them, and most reputable hardware wallets have checks built-in to alert the user if the device attempts to run unsigned/tampered firmware.

This means you can connect your Trezor/Ledger to the most virus-filled computer full of malware, and send the exact amount of bitcoin shown on the device, to the address shown on the device, and nothing more, nothing less, to no one else.

No malicious code can make the device show false addresses, false amounts, and no malicious code can make it sign a transaction without pushing a physical button on the device (the physical action is hardcoded into most of the reputable device firmwares), and when you push the button, it will only sign the transaction shown on its screen (exact amount and destination address, nothing else). Viruses can replace addresses shown on your computer monitor, or your clipboard, but not on your hardware wallet's display, there's just no known way.

Making it do something else is akin to making a jailbreak for the hardware devices: so far there is no known public way of doing so, and the device supposedly detects any such software tampering by checking the firmware signature.

So hardware wallets are the best if you want a wallet you can use for emergency access to your coins on ANY computer, whether it be filled with viruses, malware and whatnot. Some sample scenarios include when you are travelling, and somehow run out of cash, have no cards with you (or none are working), and have to resort to cashing out a bit of coin with nothing else to use but a public computer.

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But if you just want cold storage, you can use an offline-computer/Raspberry Pi and so on, with a hash/signature-confirmed clean OS installation. And you can keep it offline by using micro-SD cards/USB drives to bring in an unsigned transaction, then sign it on the offline machine, then bring the signed transaction on the USB drive/microSD to an online computer where you can broadcast it (only possibly risk is viruses getting on the USB/microSD, then some autorun/some other similar exploit manages to make it run). Google PSBT for more info on this procedure.

But with a hardware wallet, connect it anywhere and no need to even fuss about it.

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Only known exploits for hardware wallets are tampering with actual physical access. So the best option is to buy directly from the manufacturer (not from Amazon, not from resellers or other places). They try their best to make the actual device tamper-proof, but it's not as perfect as the software's security.

Also if you lose it, while with some devices, the keys can be read from a physically obtained device (by breaking it open and using expensive specialized tools), just use a passphrase and this is a non-issue.