I looks like you modified a picklist that's used in multiple places. You can see where all a picklist is used by clicking the "Usage Stats" button on the Picklist setup page in the AdminUI.
You need the two picklists to display differently in these two places. There's no way to define separate display values for two fields that are both using the same picklist.
Depending on how you build that you may need a new validation object for your customized picklist, or you might need just an extra column in the validation object for the customized Display text.
This concept worked. However I ran into problems that may (or not) be related to the fact that I created a separate business object from which I created the new pick list. To resolve this, I simply added a field I called isProject to the original business object. It was a 1 character field that holds 'Y' for projects and 'N' for incidents. With this field as my constraint filter, I was able to create two distinct pick lists with record entries targeted to meet the selection needs for each pick list.