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suffering caused by oneself=single relationship=easy to control=lord god=eternalism.
one's suffering caused by another=non relationship=hard to control=no avijjā&taṇhā to becoming/born=nihilism.
Those above all are impossible, so buddha taught paṭiccasamuppāda after denied acelaka kassapa's self view.
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They're two wrong views which the Buddha wishes to quash. Sometimes they're referred to as 'extremes', but I think the problem is simply that they're concepts which jump into our minds from time to time and usurp the reality lying before us.
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The eternalist view affirms self; believing the self (rather than the element of ignorance) causes suffering.
The annihilationist view both affirms & denies self, blaming another self (rather than the element of ignorance) for causing to suffering to oneself.
Both are self-views.
Eternalism & annihilationism are both self-views (rather than views about continuity of life).
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I think this passage can be understood by recognising that the Buddha is speaking about the fruits of kamma (i.e. action, intention) across lifetimes. Think of 'He who performs the act' as a person in the present life, and 'he who experiences [the result]' as the next rebirth. So, the views boil down to i) "The person in this life [He who performs the act] remains identical, exactly the same person, following rebirth [also experiences the result]" i.e. Eternalism. And ii) "The person in this life [One person performs the act] ceases to exist following rebirth [another experiences]" i.e. Annihilationism. The Buddha dismisses both of these as false views, but does not spell out what actually happens. I guess one possibility, based on the implications of conditionality (Pratītyasamutpāda), is that some aspect of our consciousness is reborn (i.e. Annihilationism is false), but that it can change, evolve, based on previous kamma and can even be destroyed (i.e. Eternalism is not true). But this conjecture goes beyond the Buddha's words and it would seem that he avoided, or would not declare his position on, metaphysical speculation. With kind regards - Peter