1. When the paper is published in a conference proceedings with a conference proceeding publisher then is a conference paper
2. There are some journal that published conference proceedings, it will only show at the top of the paper, the particular conference that the journal published their proceeding papers. This means that the particular paper can be call a journal article
No sir. Ideally conference papers are compiled in a proceeding. But some organisers could have their own journals or liaise with some publishers where papers presented in a conference are published after 'extending'
the content or in the form it was presented in the conference. When this happens, the new version is a journal paper. While the previous remains a conference paper.
On occasion the best papers can also be selected to be part of a book following the conference - the so-called conference proceedings collection of chapters. In terms of usefulness for promotion - if that is of interest to discuss at all - a book chapter is less worth than a scientific journal paper. But I can only speak from the perspective of a mathematician - how the prestige varies in other fields I cannot comment.