Does a transaction between two accounts of an Ethereum Wallet cost fees?

Question

I've read http://ethdocs.org/en/latest/contracts-and-transactions/account-types-gas-and-transactions.html, but just to be sure:
If I want to transfer an amount of ETH between two of my accounts (or between the Main Account Etherbase and a 2nd (3rd etc) account) in my own Ethereum Wallet (currently v0.9.0) do I need to pay gas?
(Up to date my Wallet is empty so I couldn't even try to transfer ETH inside my Wallet. Would like to transfer some ETH from kraken but Ethereum Wallet syncs VERY slow.)

Answer 1

Every transaction that modifies the state of the Ethereum blockchain cost fees, or gas. Gas is the price charged by the Ethereum system to prevent wasteful computation, since all smart contract code runs on all of the 25,000 nodes.

According to the Ethereum Yellow Paper, every transaction costs at least 21,000 gas.

• 21,000 gas currently costs $0.033 right now at the average gas price or 4 Gwei.
• You can also pay .4 Gwei for a longer confirmation time (this should work if just sending value to yourself) which will cost $0.003.

Answer 2

Any transaction between two addresses is written in the blockchain ; you have to pay fees to write any transaction in the blockchain.

Anyway, there exists no way to distinguish between two addresses of the same person and two addresses of different people, as addresses are anonymous.

Moreover, the fees are necessary to ensure that no one is breaking the system through spam.