Not sure if I understand correctly. Say I buy coin from Coinbase / Localbitcoins. If I want to move what I just bought into another wallet, it will be charged?
Why?
Yes. Because any transaction that hits the blockchain is subject to fees to pay for the proof of work the miners are doing to confirm the transaction.
If you were to move money between wallets within Coinbase, Coinbase may be able to do that without causing a transaction...but this is only because they are an exchange and don't actually keep your Bitcoin in your wallet address.