1. Forensic science = science relevant to the judicial system. Like CSI.
2. Forensic psychology = legal-system-related psychology. Like the personalities of serial killers.
3. Computer forensics is about using computers in the legal system.
4. Yet forensics by itself = public speaking.
Huh?
The first teachers of oratory were the ancient Greeks and Romans, namely Aristotle and Cicero. When they were classifying “kinds” of oratory, they termed the kind of argument used in a court of law to prove or disprove past events “forensic” argumentation. Centuries later while universities were still teaching all the forms of argument, students decided to take it to the competitive level and began debating for sport in an activity they named “forensics.” Today forensics includes competitive dramatics and public speaking.
https://www.morainevalley.edu/forensics/etymology.htm
The root is forum, which I think is used in the sense of a public place for discourse, where decisions might be made based on speeches. #4 is clearest — public speeches are proper to the forum. Similarly, anything to do with legal pleading is a public and thus forensic matter.
Thanks for the explanations, Varangy and Benquo.