Assuming you have the center section on a bench, the cone type sg bolts together from the ring gear side (another series of bolts inside of the ring gear bolts), the clutch style sg bolts together from the opposite side of the ring gear.
I'm not sure on the buttons (I've got a locker in mine) but I THINK the clutch uses a separate button that can be there or not ("not" is definitely an oops), I think the cone type has a fixed button.
I'm SURE that somebody here that knows more than me will chime in.
Edit: the button is there, so that both axles have something to push against for bearing adjustment. If you run "green" bearings, you don't need the button. And it really doesn't matter which side the adjuster is on.