The privacy of a crypto-coin regardless of whether it is privacy focused or not depends on the type of a crypto-wallet used to store the coin.
There are 3 general types of crypto-wallets - an exchange wallet, a wallet by a commercial wallet provider, and a private wallet.
An exchange wallet has the lowest level of anonymity and the private wallet - the highest level of anonymity.
For more on the 3 types of wallets please check this article -
What do I need to know before creating a blockchain wallet