I try to explain my thoughts about it as easy as I can.
It all starts with believing in any sort of self. Then there can be two ways of thinking about such a belief. Either there is a self which is eternal or there is a self which isn't and therefore is or will be annihilated. It's not so much of importance whether somebody thinks a self lives forever or dies after some time and will be born again and dies and will be born again to belief in a self which is eternal. As well as it's not important whether somebody thinks a self isn't at all or won't be anymore in the future to belief in a self which is or will be annihilated. I suppose these both views are nothing but an extension to the underlying atta-vada an go hand in hand with it. It becomes more clear the more one understands what atta-vada means. It is the clinging, grasping to the aggregates and believing a part, parts or all of them to be the self, while anatta on the other hand is not trying to tell us that there is no self at all but rather that what we consider as self (while failing to see that it) is merely a part, parts or all of those very aggregates. So the eternalist actually beliefs a part, parts or all of the aggregates, which the eternalist considers being the self, is/are eternal while the annihilationist actually beliefs a part, parts or all of the aggregates, which the annhiliationist considers being the self, isn't at all or will be annihilated.
at least that's what I think...
best wishes, acinteyyo
Thag 1.20. Ajita - I do not fear death; nor do I long for life. I’ll lay down this body, aware and mindful.