Can one shipping zone cover several states or countries?

Yes. A zone can have as many regions as you need:

1. Go to Plugins → Shipping Zone and click Edit on the zone.
2. Under Regions, click + Add region once for each place.
3. In each row, pick the Country, then the State. Leave City and Pincode as Any to cover the whole state.
4. Click Save zone.

A customer matches the zone if their address fits any of its regions. To cover whole countries, set only Country and leave the rest as Any. Grouping places this way also helps if your plan limits how many zones you can create.