Did you mean Camus's and Camus' have the same pronunciation?/kæˈmuːz/
The final letter 's' in his name (/kæˈmuː/) is not pronounced, so for the possessive you just need to add a /z/.
I was taught to use s' rather than s's.There's only one word with only one pronuciation. You're asking about the two different ways of spelling it.
In my view, the way to spell it is Camus'. Spelling it as Camus's seems quite silly to me. As I said, the final 's' in his name is not pronounced as an /s/ sound so there's no reason to add an extra letter 's' in writing.
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