That’s not a difference I would phrase as “simply”. The sense of self is something very subtle and profound. And it makes a big difference to how one perceives suffering and its ending. If you have a sense of self, you belief part of you will come to an end. If you don’t, then it is only impersonal things, only suffering, that comes to an end.
If you do have a strong sense of self, the two may feel the same, which is why some people are said to have reacted as follows after hearing the Buddha’s teachings on cessation and nibbāna:
They think, ‘Whoa, I’m going to be annihilated and destroyed! I won’t exist any more!’ They sorrow and wail and lament, beating their breast and falling into confusion. That’s how there is anxiety about what doesn’t exist internally. [i.e. about a self which doesn’t exist] (MN22)
The path is about removing all sorts of craving, including the craving for the goal itself, whatever that goal may be. So if you have any kind of “helpful” craving along the path, it should be craving to end craving! If you practice like that, you follow the eightfold path without any craving for existence or annihilation.
And ideally the practice towards awakening is not driven by craving, but by disillusionment (nibbida). See for example Dhp278.
All that is created (or “conditioned”) is suffering.
When you see that with understanding,
you get disillusioned with suffering.
That is the path to purification.
And I would also say craving for annihilation is rare in people, anyway, generally speaking. Most people would prefer to keep existing in some way, including those who see final nibbāna as the end of the khandhas. So they also still have primarily craving for existence, even though they don’t really aim at existence.
PS. To clarify my previous post, the ending of existence that aligns with the path the Buddha didn’t call vibhava, which is the word annihilationist used. He used bhavanirodha, ‘the cessation of existence’. In AN10.7 Sāriputta says: "Extinguishment is the cessation of existence.” (‘Extinguishment’ translates nibbāna, here refers to final Nibbāna.)