Minecraft Java Edition – How to Add Plugins to a Single Player World

AFAIK, there is no difference between "map" and "world."¹

You can generate new maps/worlds for your server by renaming the "world" folder that is in the same directory as your server. When you start your server, it will see that there isn't a world named "world", and will create one.

¹Note: There is now a map object in the game.

The world data, which also includes player inventories, is saved to a folder in the current working directory of the server.

The name of said folder depends on the level-name setting in server.properties, and defaults to world. Thus, you can start a new world and toggle between the saves by simply changing this setting.

Vanilla server commands related to saving/backups:

• /save-all - forces the server to save.
• /save-off - disables saving. You should definitely execute this before making a backup of a running server to ensure that the server doesn't save while you're copying, which could result in a corrupt backup.
• /save-on - re-enables saving.