If it is a lookup field, the data type should be of Lookup type as well right.
Find below the screen which has the option of "Lookup" while creating the attribute.
Once you have a lookup attribute, you will have the option as "Browse" & "Drop Down" as display type.
But if you have the an attribute with String as datatype and width as 20, the width of the attribute should be smaller than the one what you have shared.
Can you please let us know if you are observing this issue with every String attribute ?
Regards,
Srikanth G