I've noticed that one can obtain D-terms either by integrating a vector superfield (the vector multiplet) over superspace or by integrating a Kahler potential over superspace. In both cases we get functions of the D-auxiliary field (albeit different functions) that contribute to the Lagrangian density. A subsequent integration over space gives the action contribution.
Similary we can get an F-term either by integrating a chiral superfield over superspace or by integrating a superpotential over superspace. These just lead to different functions of the F-auxiliary field for the Lagrangian density contribution. Again, integration over space then gives the action contribution.
So it seems to me that we have two different types of D-term and two different types of F-term depending on whether we choose to write our lagrangian density in terms of superfields or in terms of Kahler/Superpotentials.
Is it correct to say that it is strictly one or the other? In other words we couldn't have a Lagrangian density containing a vector superfield as well as a Kahler potential, thus resulting in two separate D-terms when these are integrated over superspace.
Is there some relation between the superfield approach and the potential approach that I'm missing? Why use the two seperate approaches at all?