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As far as I know, wallet stores private and public keys and calculate balance according to that. Suppose a wallet(Single cryptocurrency) has 3 keys (private,public). Wallet will find UTXO's connected to those keys and display balance on your wallet UI.

But if a wallet handles different cryptocurrencies, how does it distinguishes between different cryptocurrencies? How does it know available public address belongs to a particular currency (Blockchain)?

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Typically there's a seed which is displayed as a sequence of 12-24 words that is used to derive addresses/private keys in different chains. Different coins use different derivation paths which are hardcoded in the wallet so even if two coins use the same address format the generated addresses will be different.

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