How does Reciprocity works

Hi, I want to know how reciprocity works. I am planning to move to
Washington from Illinois. I've noticed they have this new online Nursys where you can verify license online with few participating states. How long is the processing of reciprocity of RN-license? If I can get a license in Washington through reciprocity, will my license in Illinois still active so that would mean I will renew two licenses during the renewal period? Thank you.