There’s a difference between private & public #cryptocurrency.
Public blockchain-based cryptocurrency offer some degree of anonymity cause users to operate under pseudonyms. Anonymity and Pseudonymity are not the same thing as privacy. Transactions can be traced.
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Privacy comes with advanced cryptography.
There are popular tokens designed to be private by default by hiding transaction details.
These cryptocurrencies are public but transaction information is obfuscated in varying degrees to protect the privacy of the end users.