I didn't think it would be this difficult to find a picture or diagram of a dog clutch on the internet - think of a gear, but instead of teeth on the circumference, they are on the flat end face, now take two of those and position them so the teeth on one, fit in between the teeth of the other - slide them together, one drives the other, slide them apart, there's no drive.
Anyway, here's the front differential assembly from the Grand Vitara, this image is in section 7E of the FSM if you need a clearer picture ...
#25 is the free wheel hub - this fits inside the differential case (#17) and has the differential pinions (#26) attached to it, the side gears (#24) are attached to the axles, and this entire assembly rotates with the wheels. There are teeth on the end of the free wheel hub, and matching teeth on the axle lock clutch, which is on the end of the left differential case (#27) - when in 4WD, the actuator pushes the axle lock clutch teeth into mesh with those on the free wheel hub locking the differential case and the free wheel hub together so they rotate as one (when in 2WD, the two can rotate independently).
Whilst it is theoretically possible that the actuator is not pushing the clutch sufficiently into mesh, and this is what's causing the slip - I would expect this to affect both forward & reverse, so the fact that it works going forward but slips in reverse is what leads me to believe, the teeth may be worn.
Just so you're aware of it - to get to the clutch, you need to disassemble the third member, and reassembly will require the adjustment of backlash (in theory you can mark the adjusters and then count the turns as you unscrew them), don't undo the pinion nut or you'll need a new crush sleeve and will also need to adjust the pinion preload - this is a job that requires some level of experience.