Good to see the pics ,, now we know what you are working on.
This diff has the axles held in by the 4 small nuts that you have already undone.
Now you need an axle puller .
This can be any sort of slide hammer (also called a shock puller) .
The axle that just slid out easy was really a bit loose in the housing.
This diff has no 'C' washers to retain the axles .The diff head comes out the front of the axle casing , once the axles are removed .
Are you going to replace those thin brake linings too ? smile