Is writing a book chapter equivalent to writing a book or journal article? Can you consider yourself as an author of a book when you only written a book chapter?
Concerning your first question: Book chapters, if written by different authors, are very often similar to journal articles. But this depends on the character and content of the book.
Concerning your second question: Usually you are not the author of the book if you wrote only a chapter. However, when there are only a few authors of the book, and each one have written one or more chapters, they together can be indicated as authors of the book on the title page. There are various models for this, and it depends on the number of authors, the editor(s) and the publisher.
A follow up, is their a hierarchy among these papers? Like journal article is more given importance by universities compared to book chapters or a book.
In academia, the traditional hierarchy is that journal articles are considered the most prestigious form of publication, followed by book chapters, and then books. This is because journal articles are typically peer-reviewed, meaning that they are evaluated by experts in the field before being accepted for publication. This process is considered to be more rigorous than the review process for book chapters or books. Additionally, journal articles are often seen as more specialized and focused, as they are published in specific journals that cater to specific fields of study.
However, it's important to note that the hierarchy of publications may vary depending on the field of study, and some fields may place more value on book publications than others. It is also important to note that the impact factor of the journal, the author's reputation, the relevance of the research, and the interest of the public are also factors that play a big role in the perception of the importance of a publication.
It's also worth mentioning that while journal articles are considered more prestigious, they are not always the best way to disseminate information in certain fields, especially in the humanities or fields that require long-form analysis or historical context that cannot be provided in a journal article. In such cases, a book or a book chapter is considered the best medium to share knowledge in the field.
It hard to make generic determination and to say article is more important than book or vice versa. It depends on the quality of the articles. Let me provide several examples: Ludwig Prandtl publish is boundary layer theory in article that make a revolution fluid mechanics. On the other hand, my advisor Eckert published a book 100 year ago on heat transfer that change the way heat and mass transfer taught and the research is conducted. A thesis of Meyer changed the way compressible flow is analyzed. These are free thinkers who changed the their field. On the other hand, we have people with papers that I call dust collection and negative papers even though they might a thousand citations are either wrong and meaningless or do not provide any real contribution. I can list you many papers in ship stability and fish locomotion etc. For example, G L from Harvard university paper with over thousand citations which violates the second law thermo. Everyone accept that most introductory text books are collection of accepted knowledge without a special breakthrough written mostly by senior professors. However, I have encountered in several books which contain breakthroughs. for instance, I have to used my book to solve a problem that the only place in the world that explain it was in my book and it was unique solution. If you compare dust collection paper with a mundane book i would say that in most cases book is higher in the hierarchy. If you compare only a single chapter with a paper is a tossup. On personal, I prefer to write books because it provide a platform to make revolutions in science and I have done so. All my books are revolution in and of the field.
The short answer to your question, I think, is no. Many people might have this confusion also and it depends a lot on your organisation/employer. Most seem to regard journal articles as more prestigious as it conveys information quicker and are peer-reviewed (in reputable journals), as Syed Walli Husnain says.
The quality is also an important consideration, as mentioned by Genick Bar-Meir .
Interestingly, my employer seems to do the opposite to a lot of others and thinks that book chapters is worth more than journal articles. There are very few organisations with this view.
The answer to the first and the second question is no. In some areas and countries writing a book or book chapter may be equivalent to writing an article.