Why do different meters show different voltages between hot and ground?
Any time you see wack-a-doodle voltages associated with safety ground, you should consider that safety ground might not be connected to anything. 

It's very common in pre-1965 homes to have the original wiring laid groundless with contemporary /2 no-ground cable, and then in the 1970s and onward, extended with /2+ground cable.  Typically they either connect the extension ground to nothing (preferred), or to the metal boxes (bad, since if it isn't connected back to the panel it only causes those locations to share their ground faults, energizing all their grounds if one has a ground fault). 

So when you see a hot-ground reading like that, you are best off investigating why that safety ground is not properly connected back to the main panel (or maybe the hot is not properly connected).  If the wiring is old enough that it simply isn't connected, then furl up the ground wire in reserve for the happy day when ground is retrofitted, and do your best to insulate it from touching the metal box.