Is there a difference between the way Harmony-G and HarmonyControl Guitar process signal for harmony data?
The answer is: yes, but there's more.
On the nuts and bolts level, HarmonyControl Guitar and Harmony-G (XT) operate the same: you use a guitar to control harmony.
On a more precise level, the Harmony-G (XT) has a newer harmony algorithm and it may pick more appropriate harmony notes in even more songs. Also, Harmony-G (XT) doesn't translate to MIDI before guiding the harmony algorithm, this is only a necessary step for HarmonyControl because it is controlling external devices.