As far as Bitcoin and Monero goes (those blockchains with a UTXO model)
"coins" usually refers to those utxos (Unspent Transaction Outputs).
Those utxos are basically destroyed when they are transferred to another address and new utxos are created with the receiver.
you can imagine it like you have gold coins of various sizes (utxos of different numbers of sats in different addresses).
When you make a spend, the wallet combines one or more of your utxos to create the transaction of the amount you are spending. It "melts" down those coins to get one of the right size.
A new utxo (coin) is created in the receivers address of the amount sent.
The surplus amount is returned to you as change.
Now as far as tracking goes, this combination and transfer of utxos is written on the chain. With Bitcoin it is completely transparent, which means if I send you some sats I can look up the address you gave me to see how much is there.
You can also look at the senders address and see if theres any history there. Maybe I've combined a lot of "coins" in that address.
anyway, so there's a whole field if analyzing the movement of utxos, figuring out when people are spending, when theyre consolidating what they own themselves and general probabilistic tracking. It's a massive business these days.
Hope that helps.
