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Please provide a simple explanation that can distinguish Monero unlinkability and untraceability.

Is it possible for a cryptocurrency to have one (unlinkability or untraceability) without the other? Or is there a mutual reliance between the two?

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With Monero, unlinkability means that you can display your receiving address publicly yet all payments made to this address cannot be linked to it.

This phenomenon is accomplished with the use of one time use stealth addresses for every single transaction.

Monero untraceability is provided by ring signatures each transaction uses multiple cryptographic signatures controlling multiple outputs to mix with the outputs of the sender. An observer cannot tell which outputs are controlled by which party providing untraceability (and plausible deniability) for everyone included in the ring signature.

It is possible to have unlinkability without untraceability. In fact there are many coins that offer one time use stealth addresses. Monero (and other CryptoNote currencies) are different because the use of stealth addresses is automatic and mandatory. If one time use addresses are not used every time, user and network privacy is decreased. Monero makes it easy to obtain a high level of privacy by automating this process at the protocol level.

Ring signatures did not exist in any cryptocurrencies until it was introduced by CryptoNote. There are technologies that used mixing (CoinJoin) to make tracing Bitcoin (for example) transactions more difficult. However more difficult tracing is not the same as untraceable, particularly with the rise of companies offering blockchain analysis tools such as ChainAnalysis and BitCluster

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