There are no that big differences.
- Both words are used to describe something that has been called already.
Ich habe gelbe Schuhe. Klara trug dieselben gestern. -> I have yellow shoes. Klara wore the same (shoes) yesterday.
Ich habe gelbe Schuhe. Klara trug dieselbigen gestern. -> I have yellow shoes. Klara wore the same (shoes) yesterday.
- Or if something happens at the same time:
Ich gehe zur Schule. Kai geht zur selben Stunde zur Schule. -> I'm going to school. Kai is going to school at the same (hour).
... Kai geht zur selbigen Stunde zur Schule. -> has the same meaning.
__
I could make many more examples but the word selbe and selbig got the same meaning in the most cases.
But you have to know that nobody use selbig anymore. Except some very smart guys or a editorial team at least. ^^