It's hard to give a precise minimum amount of copying that constitutes plagiarism, and there are always various subjective mitigating and aggravating circumstances to consider. Ultimately, though, any official response to plagiarism should come from an organization that has a statement about what they consider to be such.
In this case, the latter article is published in The Astrophysical Journal. The publisher's ethics policy has the following points to make (all emphasis mine):
Plagiarism is the act of reproducing text or other materials from other papers without properly crediting the source. Such material is regarded as being plagiarized regardless of whether it is cited literally or has been modified or paraphrased.
Thus here the standards are pretty loose; even inexact copying counts. Certainly a change in one equation does not make this non-plagiarism.
Deliberate refusal to credit or cite prior or corroborating results, while not regarded technically as constituting plagiarism, represents a comparable breach of professional ethics, and can result in summary rejection of a manuscript.
Even if there was no overlap in text, loose or exact, omitting something you know to be relevant is just as problematic.
Strictly speaking, authors are not formally required to cite unpublished or unrefereed materials, especially in cases where the veracity of the unpublished work may be in question. However, when principles of common professional courtesy dictate that such attribution is appropriate, authors are expected to honor these conventions.
Here's where that subjectivity comes into play. It's not clear how refereed the earlier work is, nor what level of "professional courtesy" is considered "common." Conference proceedings are rather rare in astrophysics, especially in the US (where the latter article is published). Most conferences are for oral talks and posters, not written papers. To the extent conferences do catalog what happened in a permanent way, one still looks to cite "real" articles rather than proceedings.
Does a proceeding count as prior work? Does it matter (with regard to professional courtesy) that the first article's intended audience was probably largely confined to Korea? These are questions that ultimately the publisher must answer, and I could find no statement of theirs addressing them.
The community or its practitioners are also free to develop their own opinions and take whatever action suites them. For example, a tendency for self-plagiarism will get a researcher noticed as producing water-down rehashings of old work and will thus lead to people not paying much attention to that researcher in the future.
The issue of authorship is only loosely related. In astrophysics, authorship is understood to be in order of significance of contribution, where in cases of large author lists people at an equivalent tier of contribution will be ordered alphabetically. At some level, there's no way to reliably tell who really did what, and so unsurprisingly I could find no official statement from ApJ about author order.
The fact that the bulk of the content of the latter paper was written by the second author years ago would seem to be strong evidence that the authorship norms of the community are not being followed here. A journal has every right to object to this (or any other feature of a submission), and maybe they would take action if notified, but I cannot be sure. The practice of gifting authorship, either to help students' careers or to help one's own, is thankfully not so common that strict guidelines have been set up to deal with it.
Finally, an update on this particular case. The journal was notified of the earlier article, and it has indeed issued a retraction for plagiarism. There does not seem to be any mention of gift authorship one way or the other.