A user is mid-swap, the wallet prompt is up, and the question is the same one it always is: wrap the native asset, or mint a synthetic version on the destination chain. Two buttons, two paths, two different ledgers to argue with later. The choice is small at the moment of the click and loud at the moment of the audit.
Wrapping is the conservative move. You lock the asset on chain A, a custodian or contract mints a 1:1 representation on chain B, and the proof of the lock is the thing you can point at when someone asks where the collateral lives. The cost is what you'd expect: a wrap fee, a redeem wait, and a counterparty to trust with the underlying. Minting skips the lock. A protocol takes your deposit and issues a wrapped or synthetic token against it, often using liquidity pools rather than segregated collateral. Faster, cheaper, and the slippage is whatever the pool says it is that second.
The number that matters is the redemption path. If the wrapped token can be unwrapped 1:1 in under a block on the original chain, you're holding a true bridge token. If the unwrap depends on a pool, a price oracle, or a third party's solvency, you're holding a synthetic, and the peg is a promise rather than a receipt. Both work until the day they don't, and the failure modes are different. Wrapped assets fail at the lock: the bridge contract, the custodian, the multisig. Synthetics fail at the price: the oracle, the pool depth, the liquidation engine.
For a Crypto Bridge between two chains you actually use, the wrapped route is the one you can reason about without a dashboard. The synthetic route is the one you reach for when speed matters more than the ability to explain the position to your accountant. Pick based on which failure you can live with, not on which UI has fewer clicks.
The cleanest example of the wrapped path, where the lock is the receipt and the redeem is the test, lives at zakariafkxu116285.thechapblog.com.