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.
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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.