cart and set aside
The assignment was not paid, so the publisher did not receive the proposal. Go to your shopping cart to finalize your order.
in progress (+ awaiting validation) and to treat
Awaiting validation, the publisher has not yet accepted the mission.
If it's in progress, the publisher is the one who has to act on it, so you don't have to do anything.
When it is to treat, you must take an action (e.g. validate a publication or respond to a negotiation).
completed and declined
A completed assignment has come to an end : publication is either planned so the article is ready but the publication date has not yet arrived; or completed, the article is online.