Source 1: We want to know the vocabulary and syntax of being, or as Rosen puts it in 'The Limits of Contingency', 'the combinatorial essence of the world'. What are the basic elements and how may they be combined?
Source 2: We want to know, as it were in advance, whether various kinds of statements that are not put in terms of the basic elements count as high-level descriptions of any possible world.
Many of Kripke's arguments that certain kinds of statements are necessary furnish considerations which purport to show that whatever the possibilities are exactly, none of them is correctly described as one in which '...'.
This mode of argumentation on Kripke's part can make it look like his modal notions can ultimately be explicated along conceptual or semantic lines. But, as Putnam came to appreciate in between 'The Meaning of "Meaning"' and 'Is Water Necessarily H2O?', this is not so.
In this connection it is notable that all of Kripke's distinctive modal theses are negative as regards possibility. (His claims, in the course of arguing against descriptivism about names, that well-known facts about Aristotle etc. could have been different, are an exception, admittedly - but for those arguments, I don't see that he needs these alternative possibilities to be real, metaphysical possibilities. The modality used in those arguments could be deflated to conceptual or semantic without affecting the arguments, which are after all for a semantic conclusion - that names aren't synonymous with descriptions.) As far as I know, Kripke never seriously argues that such and such really is possible, really is a way the world could have been. Rather, he just works on the assumption that there are many quite various ways things could have been, but then seeks to draw some limits in high-level vocabulary.
But these Kripkean results, if that's what they are, only satisfy interest in metaphysical modality that derives from the second source. How we might satisfy our interest that derives from the second source is largely left untackled, and this is one reason why many have found Kripke's work frustrating. He elicits epistemic hopes, someone might complain, without giving us even so much as a roadmap for how so satisfy them.
His suggestion that metaphysical possibility may coincide more closely with physical possibility than has often been supposed may however be suggestive. On the other hand, he is against physicalism, so this couldn't be the whole story from his point of view.