  The recent paper arXiv:1205.6881 has developed superform formulations for two
versions of the vector-tensor multiplet and their Chern-Simons couplings in
four-dimensional N = 2 conformal supergravity. One of them is the standard
vector-tensor multiplet with the central charge gauged by a vector multiplet.
The other is the variant vector-tensor multiplet with the property that its own
one-form gauges the central charge. Here a more general setup is presented in
which the known versions reside as special cases. Analysis of the setup
demonstrates that under certain assumptions there are two distinct variants,
corresponding to the two formulations in arXiv:1205.6881. This provides a
classification scheme for vector-tensor multiplets.
  We then show that our superspace description leads to an efficient means of
deriving component actions in supergravity. The entire action including all
fermionic terms is derived for the non-linear vector-tensor multiplet. This
extends the results of de Wit et al. in hep-th/9710212, where only the bosonic
sector appeared. Finally, the bosonic sector of the action for the variant
vector-tensor multiplet is given.
