Replace Field Contents can copy the value from the global field to the original non global field. One use of Replace Field Contents will update every record in your found set. This can be done as a manual menu choice or in a script run from a script trigger on the field. In such a script, the global field can be cleared after the replace has updated the non global field.
Other solutions might set up a related table where different groups of records in your original table link to the same record in the related table and then you would assign this value to a field in the related table to show this value for all the records linked to it. This enables you to assign different values to different groups of records without using a script or replace field contents.