If you duplicate frames, by adding a copy, it will duplicate the text field. If you then click on this text field and cop and paste, it will create a copy, but with a new name. Delete the origonal one, and now work with this copy, click to remove the motion effect, and you will be back to static text again, or if you prefer you can add an alternative effect. This second text will stand independant of the first. So the rule is if you copy and paste on the same frame you make an independant copy, if you copy the whole frame it makes an exact copy.
Hope that explains it.