Why do some PCB antennas have a return path to ground?
A connection to ground is a short at DC (0 Hz), but not necessarily at AC (if the circuit driving the antenna is running at a high enough frequency and has no DC offset).  That's because even small loops (causing the "short" to ground) of metal are inductors, and thus have a measurable non-zero impedance at a high enough frequency.

So one antenna system has an inductor to match the output to the antenna, and the other has an extra stub to do the match in a different way.