Getting downvoted on this. I am not complaining about the downvotes, but seriously, please enlighten me...
Signed transactions can even be shared through other channels, to be broadcast at a later time for settlement, like a check. This is how the Lightning Network functions.
Keys can be held in many forms, including purely in software, digitally inside a hardware secure element, or converted to words and printed on paper or metal.
Bitcoin even has basic scripting that allows more complex setups, such as only allowing a ledger entry to be updated after a certain duration (timelocks) or requiring a quorum of signers (multisig), so simply having a corresponding private is not always sufficient to immediately spend the corresponding funds.
In the past “brain wallets” were popular, where the private key is generated from a memorized passphrase. These are a bad idea because it’s trivial to watch addresses corresponding to every entry a password dump, and automatically move these funds whether you’re the original owner or not. I mention this to illustrate how having the corresponding private key is necessary to control funds but it’s not sufficient to prevent someone else from controlling the same funds.
On top of all this, most “Bitcoin users” leave “their” Bitcoin on exchanges, so what they really own are IOUs rather than Bitcoin itself.
Bitcoin “ownership” can be pretty abstract.
It would be more accurate to say that you can own "mathematically guaranteed exclusive control over" bitcoins.
and you that can store that mathematical guarantee on any number of cheap, readily available physical devices.
You can also elect to destroy the possibility of outside knowledge of the secret, leaving the "physical memory chip" as the sole means of humanity interacting with those coins.
Still, access isn't really possession is it. I can lend my house key to a friend but they don't possess my house. The deed is what really declares me the owner. In the case of your coins, it's the consensus of the blockchain.
Not all discussions require the highest level of technical detail.
But if you have a $100 in your bank account, there is an additional constraint – you can spend it only if your bank is alive and functioning correctly and lets you specifically (you are not sanctioned/banned) to spend it.
Same is the case with bitcoin for those who store their private key on exchanges.
First there should exist a market for it (others who also believe bitcoin has value). Then, just like banks, the bitcoin exchanges where you escrowed your key have to let you spend it through them.
If all exchanges you have access to in your country decide to ban you (because your govt told them to) then you cannot spend your bitcoin.
In this way, bitcoin and your bank account balance are similar and they both are different from hard cash in hand or gold coin in hand.
If you hold your private key yourself and run your own bitcoin lightweight node to connect to bitcoin network and submit your transactions, then you don't need exchanges. Even then, others who use exchanges maybe blocked from transacting with you through govt sanctions etc.
You can think of Bitcoin as a kind of identity management system. The blockchain stores transactions mapping public keys to each other and monetary values. As long as you remember the private key matching your public key you can issue transactions on the blockchain.
Contrary to common belief Bitcoin is not stored on your hard drive, they contain only your private keys. The monetary units themselves, “UTXOs”, are stored on the network of Bitcoin nodes distributed all over the world.
