Resignation can mean either stepping down from a job or accepting an unpleasant but inevitable situation. You could even feel resignation as you announce your resignation.
Once you've announced or handed in your formal resignation to a job, organization, or political office, you're finished. You've formally quit or stepped down. If you've left the position due to budget cuts, you'll probably leave with a feeling of resignation — acknowledging that there's absolutely nothing you can do about it.