your questions don't seem to be related to HD wallets though!
an HD wallet is simply a wallet that is based on BIP32 proposal[1]. it allows your wallet to have a master key to generate all your addresses from. and just like an address you have 2 sets of keys, a private one which you keep secret and a public one which you can put on your hot wallet or share.
for example a business (shoe store) creates a wallet offline and generates a master private key. then from that master private key it creates a master public key and transfers that to their cashier. there you can create the same addresses as if you had the private keys but you don't. so you are safe while you don't have to go back and forth between two computers for every address you generate.
[1] https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki
an HD wallet is simply a wallet that is based on BIP32 proposal[1]. it allows your wallet to have a master key to generate all your addresses from. and just like an address you have 2 sets of keys, a private one which you keep secret and a public one which you can put on your hot wallet or share.
for example a business (shoe store) creates a wallet offline and generates a master private key. then from that master private key it creates a master public key and transfers that to their cashier. there you can create the same addresses as if you had the private keys but you don't. so you are safe while you don't have to go back and forth between two computers for every address you generate.
[1] https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki
Thank you for the explanation and the link. I have used a few HD wallets without even realizing it! I never noticed that the receive address was different every time I received them
Most wallet softwares do number 1 automatically (as that's the initial design that everyone gets a new address for every new transaction).
As pooya says, you can do it with separate wallets per till and separate public/private keys too so that it is more secure.
In addition to this, you might want to wait for 1 or 2 confirmations (or treat it like an international transaction and get people to sign something when they pay with bitcoin and show proof of ID to let them have an unconfirmed transaction that you can go back and get later - this is often done with international visa debit cards for people who go to different countries within the EU if a currency conversion is needed).
You'll probably want deposits to go in in legacy addresses too, native segwit addresses might not be compatible with every wallet.
A legacy address begins with a 1.
A segwit address begins with a 3.
A native segwit address begins with a bc1.
Dang, having the customer sign for the transaction isn't much of a deviation from the current economic model. I think what the shoe store would have to do is set up a lighting network node and use lightning to receive the payment instead. That way they are on the bleeding edge, and hopefully the user experience will be impressive for the customer the first time they use it.
Thank you for taking the time out of your day to help me out, you both are definitely steering me in the right direction.