A competition doesn't live in a single edition: each season is an independent cycle with its own schedule, standings and history.
Independent editions
When you close one season and open the next, matches and standings start from scratch without losing the history of previous ones, which stays accessible from the competition's season selector.
Only one active season
At any given time there's a single season marked as current, which is the one used by default when entering the competition, generating the schedule or checking the standings.