Both InDesign and Illustrator have a File, Package feature.
Creating a Package is not the same as "Save As."
After a Save As, you end up in the new file.
After a Package operation, you are still in the old file.
If you are using File, Package to create a new version of the document, you need to close and go to the folder with the new packaged document and open it.
Generally Package is used as a final step, to transfer a file to another team or as a backup operation.