Cancelling tells your guests it's off and keeps the record. Deleting removes the event.
On the event page, open Actions and choose Cancel event. Everyone who said yes, and everyone who answered Not sure yet, is told it's off; people who said no or never answered aren't. Reminders still scheduled stop, and the event moves to Cancelled on your Events page with its answers intact.
Delete is on your Events page, in the event's menu. If the event was sent and is still on, it is cancelled first, so the same people are told. Then it goes, with its invites and answers, and the links that went out stop working.
Archive, in the same menu, moves an event to Past without telling anyone or deleting anything.
None of these charges you, and none refunds a paid event on its own: see Receipts and refunds, and write to us before deleting a paid event.