What is one way an academic argument might differ from an argument in a televised political debate?

An academic argument uses concepts, categories, data, i. e., a type of language that can only be understood by members of the field. It is not trying to be understood by everybody like a televised political debate is.

An academic argument has a different audience than a televised political debate. A televised debate has a much larger audience. An academic argument is directed to a specialized audience thus it is more complex than a televised one.

A televised political debate usually serves primarily to convince people about one or another candidate. So candidates use questions to promote their agenda and prove themselves better than the other.