Difference between account balance and the sum unspent transaction outputs I have account in bitcoin-core (for example it's "maks") and there I have 0.00010884 BTC.

getbalance "maks"
0.00010884


But when I get UTXO:

listunspent 1 999999 [...array of addresses belongs to "maks" account...]


and sum all amounts up I get 0.00009824 BTC and I don't understand WHY??
I thought account balance is sum all unspent transactions outputs. Please help me!
Or maybe it's don't need me... I want to create raw transactions and for this I need unspent transactions. How I can get these transactions?
Accounts have nothing to do with UTXOs.

They are bean counters to help you determine who owns how much, in case you have multiple users sharing the same wallet.

An account is credited whenever a payment arrives to an address associated with that account. It is debited whenever the sendfrom or sendmany RPC is used while specifying that account. If you use any other means of sending, the "" account will be debited.

However, the UTXOs are always shared across all accounts in a wallet, and don't belong to a specific account. When you send out money, all UTXOs are always considered. Accounts can go negative even, if you use the move command (which just increments one account and decrements another).

The above is one of the reasons why the accounts system is deprecated, as it does not match people's expectations. If you want to have actually separated users, with independent UTXOs and balances, you should look at the multi-wallet feature added in 0.15.0.