Pick lists are scoped to the ‘collection’ level, but the way pick lists are assigned is via the Schema Config.
This means to use a different pick list between two different collections for the same field, you need to create two separate pick lists with the same name in each collection.
While the Schema Config will resolve based on the pick list name you select, the items in the pick list are based on the respective pick list record in each collection.
You must create a new pick list record for each Specify collection in which you want to use it. It’s a bit confusing at first, so let me know if you’d like to set up a short meeting or if I can help provide further clarification!