One-way integration gets return data out of Loop. Webhook events, return updated, return created, return closed, label created, fire the moment something changes, or your system can poll the returns list on a schedule instead.
Two-way integration lets your systems act back into Loop. The Process Return API can mark a return as received and processed straight from your warehouse system, and the item grading and dispositioning APIs record a returned item's condition and what should happen to it, restock, write off, send to liquidation, without someone doing that by hand in Loop's own dashboard.
Authentication depends on which piece you're calling. A standard API key, sent in the request header, covers most read access. The Label API, the webhooks API, and the ship-by-Loop API currently require OAuth 2.0 instead.