They a different variants of the coplanar waveguide. Generally it is more common to use a coplanar waveguide with ground plane (GCPW), particularly if you have a long feedline, bends or enclosure wall very close to the board. The ground plane in a GCPW serves not only for impedance matching but also for the return current, for a long CPW feedline (without ground) this return current needs to be handled correctly.
Note that the 2 chip antennae that you listed are quite different. The first one is an unusual chip antenna that is designed to be mounted directly over a ground plane. In this case the obvious choice is a GCPW feedline. This antenna is meant for very compact designs in which not needing metal clearance under the antenna is a significant convenience. There is a catch however as the efficiency of that antenna is quite low, only 38% on a typical 1.5mm board.
The other antenna is a more common type of chip antenna requiring metal clearance underneath it and has better efficiency. In this case you can choose either CPW or GCPW. GCPW is generally preferred.
Note that the dimensions and spacing calculations for the feedline will be different for CPW and GCPW.