The person in question — the person being talked about or involved (e.g., 'ask that person').
その質問についてはその人に聞いてください。
Please ask that person about that question.
会議でその人が説明した内容をもう一度まとめてください。
Please summarize again what that person explained at the meeting.
A distinguished or notable person — an old/formal expression (used in phrases like 'その人あり').
古文で「その人あり」とある場合、特に有名な人物を指すことが多い。
In classical texts, 'その人あり' often refers to a particularly famous person.
That person — a pronoun used to refer to someone (equivalent to English 'that person').
その人は昨日帰りました。
That person went home yesterday.
その人と話してみたら、親切だった。
When I talked to that person, they were kind.