Your definition of self promotion is a bit different from what I usually think. I usually consider self promotion to be someone promoting something that that same person did. Both of your non-self-promotion examples would be self promotion under my definition.
So what you consider to be self promotion vs non-self-promotion, I consider to be self promotion with a title that very clearly indicates that vs self promotion with a title that less clearly indicates that. However, the "Show HN" phrase is only used for self promotion I think, so even without the "I", anyone familiar with the convention will know it's self promotion.
So what you consider to be self promotion vs non-self-promotion, I consider to be self promotion with a title that very clearly indicates that vs self promotion with a title that less clearly indicates that. However, the "Show HN" phrase is only used for self promotion I think, so even without the "I", anyone familiar with the convention will know it's self promotion.