I have two lists from different departments. I'd like to copy and update changes from list A in department A to List B in department B. I use sharepoint 2013, and workflow 2010.
Thank you
Do you mean different site collections by “department”? The default SharePoint Designer workflow does not look up across site collections since the credential works on a site level.
You can take a look at Sharepoint Designer Custom Workflow Activities that allows you to extend the lookup to a different site collection.
In addition, if you are open with SharePoint 2013 workflow, there is a Call HTTP Web Service action you can use for further development.
See a few references here:
Copy and update list items based on changes in another list on another site.
SharePoint Workflow - Update Item in a different Site Collection.