A prescreen is a very short (usually one page) process designed to record information about applicants before launching an intake.
Typically used by high volume call centers where one group of people will do initial screening, and a different group will do full intakes. And in this context, often used with the appointment scheduling feature.
Information gathered in this short process is carried into an intake process if the applicant seems eligible for services. If the prescreen questions lead the screener to decide the applicant is ineligible or should only be referred somewhere else, the data entered by the screener is captured for later analysis of rejected applications and/or reporting to funders that require such tracking.
Programs that don't need to record detailed information about rejected applicants probably don't need a prescreen process. They can simply inform callers or visitors that they are not eligible, or start a normal intake process if the applicant seems eligible.