I can go and get a bitcoin through blockchains (on-chain). Also I can go to any exchange (say, Binance) and buy one (off-chain). All I know is that they are different at least with respect to confidentiality (to some extent; if one knows my wallet address on blockchain, they can follow my transactions over time but not on exchange). My question is more about the difference in nature of the two coins. I imagine the legal rights can be different.
What I get on Binance is probably just an IOU instead of an actual bitcoin. For example, is there a way to transfer that bitcoin from Binance to a ledger, without cashing out the position in Binance and buying one on-chain?
In other words, are on-chain and off-chain bitcoins (or other cryptos) identical (or fungible) animals or is there a contractual arrangement by the exchanges that make them identical (for example some type of pegging mechanism inherent in the exchange design). any reference to related articles also helps
Not familair with Binance, but let me replace it with coinbase to answer.
When you buy a Bitcoin on Coinbase , they update their internal database with your ownership of that bitcoin.
If you leave that coin there, Coinbase holds the private key , and provides the security for you and keeps backups of the private keys ,
so you don't have to worry about keeping your own backups.
That being said, if coinbase was hacked your coins could be stolen, but coinbase keeps an insurance policy on the coins in their hot trading wallets, so odds are your coins would be insured for their fiat value.
or
When you buy a Bitcoin on Coinbase , they update their internal database with your ownership of that bitcoin.
You decide to send that bitcoin to an address only you have the private keys for.
You send the bitcoin to your address (This makes a transaction on the blockchain), now it is no longer insured by coinbase,
and
you are primary person responsible for making sure your private key is backed up and secured.
If you lose the private key due to fire , flood or theft/hack, you have no recourse of recovery, then your coins are just gone.
* Also if you die ,
your relatives can present coinbase with legal documents and receive your coins from the exchange.
But any coins that you did not share the private keys with your relatives would be lost forever if only you control the address.
* When you buy BTC on an exchange, you don't cash it back out to fiat to send it ,
you just send it to your BTC address, no cash out to fiat happens.
But you do have to send BTC back to an exchange before you can cash it out to fiat or another entity that is accepting BTC as payment if you want to spend it.
*Last thing, On Coinbase you can send BTC offchain to another Coinbase user at zero cost, if you send bitcoin onchain you have to pay the bitcoin transaction fees to the miners.