Copying A Project Entirely to use as the start of a new project

I am working with an existing project my coworker created.  I want to copy the entire project to use as a starting point of a new project.  I thought I did it correctly by copying the old and renaming it as a new project.  But whenever I make a change to the old project, it also updates the new...and when I update the new, it also changed the old.  I must have done something wrong.  Can someone please help guide me?