The left hand one is designed to take a positive click on hydraulic type oil gun, which works (in fitting) like a normal grease gun.
The right hand one is designed to use an oil gun with a recessed cone type fitting, such as the Wanner one that Myford supply, where the fit on to the nipple is only sealed by the positive pumping pressure made by operating the gun (and you need the gun to be exactly in line with the face of the nipple).
A grease gun fitting type oil gun will only properly fit the left hand nipple, a Wanner type gun will fit both.