The total number of coins in a chain is deterministic. If using a UTXO model, then it's the number of unspent outputs that are linked to your private key, if using the account model, then there is an on-chain state that holds your balance, your nonce and some space for code (which is how smart contracts work..).
In the case of ERC style tokens, the token issuing contract holds a hashtable that links public addresses to a token balance as well as an invariant for totalSupply.
In any case, anyone with access to a block explorer or a node can query for an address and see its balance using the provided APIs (in ethereum it would be web3.eth.getBalance('0xdeacafe')
In the case of ERC style tokens, the token issuing contract holds a hashtable that links public addresses to a token balance as well as an invariant for totalSupply.
In any case, anyone with access to a block explorer or a node can query for an address and see its balance using the provided APIs (in ethereum it would be web3.eth.getBalance('0xdeacafe')