So also the hardware wallets have a security chip which has been proven to generate a key that is random. Although there are some who are paranoid about even those chips being "random enough" and those people generate their phrase using dice and the diceware lookup table. The seed phrase is just a friendly way of representing the actual 256 bit hexadecimal string which Bitcoin core actually uses.
Discussion
I get generation thing. What I'm not getting is how you can possibly "receive" BTC to that address/whatever without going on line. You have to go online at some point to interact with the blockchain. Since that is the case, what is the point of having a hardware "wallet?"
All the private keys and associated addresses already exist. You don’t create them, you find them. You can do that multiple ways, by hand, with software/hardware, or combination
If they already exist, how can you claim to access one, if not ONLY by going online and signing transactions?
You can receive without ever going online. But yes to send you need to sign a transaction and send to mempool
How can you "claim" an address as yours without going online? Your saying someone can just pick random addresses and send a bunch of BTC to them, and anyone who derives that address can go "get" that BTC? If that's the case, can't more than one person try to claim it?
Theoretically yes. You don’t claim private keys and addresses. Theoretically someone could randomly generate your same private key. But there’s some sufficiently large ( like more than the amount of atoms in the universe or something?) number of private key pairs to where both of those things are, in practice, impossible
Also, I am no expert, but this is my understanding.
That's what I also understand, but, gosh... That makes me feel a bit squidgy about the whole thing...