Bentley Map Help states:
The Value Col Name is the column from the query that will actually be stored in the property.
The Edit Column name is the column from the query that will be displayed in the combo box.
That means the:
Value Col Name is the stored value which displays in the Search dialog, Data Browser, Thematic, Export to file, and Post to database.
Edit Col Name is the displayed value for PBA, Labeling, XFM Place and Edit Dialog, Analyze, and Element Info.
For example, the following Domain List has several columns describing various minerals:
In the feature definition, the Value Col Name is set to Col1 which describes the colour.
And, Edit Col Name is set to Col3 which provides the mineral name.
During feature placement, Col3 is displayed in the Place Feature dialog:
However, the values from Col1 are used in the Data Browser.