I am wondering which are the conceptual differences between \subject and \startsection ... \stopsection commands. From my document's compilation I can see a that the former produces an "unnumbered" section. So, the purpose of \subject is to replace \section*{} in LaTeX? If that it's the answer, then can I include \subject's contnent into TOC?
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You are perfectly right that \subject is just an unnumbered \section in ConTeXt. The reason is that there doesn't exist a thing as starred commands in ConTeXt. One could have has \unnumberedsection instead but then who wants to type that?
All the default sectioning commands are listed on the Titles page in the Garden.
On the Table of Contents page in the Garden there are instructions on how to get unnumbered sections to appear in the table of contents. It is very easy and a minimal working example is shown below. The list parameter in \setupcombinedlist can be extended with all kinds of other sections like, e.g., subsubsubsection.
\setuphead [subject] [incrementnumber=list]
\setupcombinedlist
[content]
[list={chapter,section,subject,subsection}]
\starttext
\completecontent
\startsection[title={Test section}]
Lorem ipsum
\stopsection
\startsubject[title={Test subject}]
Dolor sit amet
\stopsubject
\stoptext
