対談, as least in modern Japanese, almost specifically refers to a talk session between two celebrities in the format of a talk show or a (mutual) interview. The topic is generally casual and not very socially important (e.g., their personal work style or motto), and hot debating is not intended. In a typical 対談, the two celebrities talk with each other, sometimes like an interviewer and sometimes like an interviewee. 対談 is a very common format of a magazine article.
Here is a typical 対談, one between a Nobel Prize winner and a shogi (Japanese chess) champion: ノーベル賞学者と史上最年少四冠のスペシャル対談!!
The two people selected for a 対談 are typically unrelated in their everyday work. Sometimes, there is an unnamed third person who plays the role of a host and provides various topics, but the main actors are always the two celebrities. If one of the two is an unknown writer, it is simply called an インタビュー. If three or more celebrities are present, it is usually called a 座談会. When politicians and such engage in serious discussion, it is called a 会談.
会話 is just "conversation"; this is something ordinary people do every day.