Normally, when you refer to a court case in a real court, you would state not just the name of the case but also the remainder of the citation for the case, e.g., Brown v. Jones, 485 P.3d 875 (Colo. 1995). This is necessary, because there may be many cases out of the many thousands or millions of reported cases with parties with the same surnames or business names, especially in criminal cases (where one party is always "The People"), and in litigation against government entities or other repeat litigants (e.g., mortgage companies and credit card companies).
But, since it isn't a real court and the moot court process often works from a pre-established list of precedents that can be fully distinguished from each other by the party names without the rest of the citation, moot court allows the parties to dispense with this fussy detail that isn't necessary in this pretend court environment if a participant lawyer requests that this be done. Once permission to do this is secured, a case can be referred to as, for example, Brown v. Jones without the balance of the full legal citation.