Y/ZWallet supports one or many accounts. Each account has a shielded and transparent address (unless it was restored from a secret key).
An address has zero or more notes. For shielded accounts, notes are encrypted and only visible to the account owner. Transparent addresses have notes in cleartext.
A note is conceptually an “I Owe You”. It can have any amount greater than zero (including zero). The account balance is the sum of all the note amounts.
When you pay, you take one or many notes and spend them to create new notes that the recipient can later use. This forms a transaction.
Transactions are broadcast to the network and relayed between nodes. Eventually, they are picked up by a miner that includes them in the blockchain.
Until then, a transaction is unconfirmed. If a transaction is in the latest block, it has one confirmation. If it is included in the previous block, it has two confirmations, etc. The more confirmations it has, the less likely it can be reverted.
Notes are always fully used. They cannot be split. In practice, it is not an issue because you can create new notes for yourself. For more information, check the UTXO entry in Wikipedia.
The app displays the various elements mentioned above in its UI as follows: