The /connections endpoint https://docs.li.fi/li.fi-api/li.fi-api/getting-all-possible-connections provides an overview of routes that should be possible under ideal conditions. It can be used to limit shown options, e.g., if there is no connection at all between two chains using a certain bridge.
When quoting a specific route, more information is present that will filter the possibilities further
e.g.
- amount: can the bridge/DEX actually swap that amount
- 1 step / 2 step route: which limits if an exchange on the destination should be used or not
- wallet/contract used: accounts for specific limitations
- availability of the bridge/DEX API, etc.