Everlasting VS Never-ending

Well, those expressions mean exactly the same thing, when it comes to describing something whose end is unforeseen, cannot be anticipated. Nevertheless, there is a subtle difference that may not be clear to the foreign speakers of English.

We can say everlasting love (there's a song named so), but when love turns into suffering, we may undergo a never-ending pain.

The conclusion we can draw upon it is that, never-ending is a phrase commonly used to denote something unpleasant, that does not seem to have an end.

A special note to the word eternal, that of broader meaning, describes something whose both beginning and end are unknown, lasting or existing forever.