As I show you in my book, you need to duplicate, not copy your title.
To duplicate, right-click on the title in your Project Assets panel and select Duplicate.
Copying produces a clone of your title, and any changes made to one are made to all clones.
Duplicating produces a separate file identical to the original that you can edit separately from it.
I have not found the principle and procedures for Classic Titles to be the same as those for the Motion Titles for Premiere Elements 14 Windows 64 bit.
I confirm your results where you clearly state you are using Motion Titles and have looked at both Copy/Paste and Duplicate Results. If you use the Duplicate approach on a Motion Title, you change the text in the Duplicate, you change the text in the Original. I am not sure how to overcome this other than to create a new Motion Title for the second instance.
As for Saving the Motion Title. Problems have been reported for that. That has met with mixed results. Motion Titles has a different means of saving than does Classic Titles. See Save As New Title in the feature. That action is supposed to save the Motion Title to Motion Titles Custom under the Titles & Text Tab. The Classic Titles get saved to hard drive as prtl files.
I find that my duplicate button is greyed out under edit and when i right click the edit button is greyed out. I am us premiere elements14. Why are they greyed out?