Normally, one has the standard two jacks (one for the headset and one for the mike).
Single connectors tend to be either military (or ex mil) or they are used on aircraft-powered ANR headsets.
For example, the Bose X headset can be obtained with jacks (with an inline box with a battery in it) or with a single multipole aircraft-power connector (with the headset being powered from the aircraft - much better)