The pair styles you mention (coul/…/soft or tip4p/…/soft) contain just the Coulomb part, analogous to the pair style coul/cut, etc. Their purpose is to be combined with a repulsive part.
Full pair potentials are available in pair styles lj/cut/coul/long/soft, etc. for those applications using typical repulsive+dispersive+electrostatic potential combinations.
The core-softed versions are just modifications of existing pair styles, so it is a good idea to read the man pages for both.
Hope this helps.