To pass a token from chain A to chain B, what the bridge does is block the token on chain A and mint a new token on chain B, that is, new tokens of the same amount are created on the block chain receiver, when redeeming the assets, the equivalent tokens are burned and then the original assets are unlocked. This prevents assets from being used on both chains at the same time.

That's very true, the wrapped token would be burnt at the end of the contract to make sure users don't have two tokens and spend on the blockchain. The type of bridge you explained here is wrapped assets bridge.