A bitcoin address, or receiving address, is like a digital mailbox slot - anyone can send bitcoin to you through your bitcoin address. Modern Bitcoin wallets automatically generate bitcoin addresses, typically when a user clicks on “receive” or “bitcoin deposit”.
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A bitcoin wallet is a piece of software that has access to all the bitcoin received via your bitcoin receiving address(es). You have to use your private key to transact funds in your bitcoin wallet. Your bitcoin private key is like the key that opens your digital mailbox slot, allowing you to access your funds from anywhere. A private key is given to you whenever you set up a bitcoin wallet.
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If you are interested in learning how to set up a bitcoin wallet, click here.