The term "podium" is used correctly to refer to the horizontal surface upon which a speaker, conductor, or other such person stands; while such surfaces are often higher than the immediately-surrounding floor, the term "podium" may refer to such an area whether it is raised or not (one may think of the area as having "elevated importance").
Because the term "podium" is often used in rooms where the speaking position does not have a raised platform, but does have a lectern (bookstand) in front of it, and since "going to the podium" in such a room would imply walking behind the lectern, many people have come to interpret the term "podium" as referring to the lectern rather than the area behind it, and will thus use the term "podium" to refer to the former (e.g. "place the books on the podium"). Note that a construct like "take the books to the podium" would be perfectly reasonable if they were intended for use by someone standing on the podium (behind the lectern) as would typically be the case.
In cases where the standing surface area behind the lectern is physically higher than the surrounding floor, the term "rostrum" would be appropriate, but it is not appropriate when there is no raised floor. The term may be somewhat less subject to misinterpretation than "podium", since it refers to the platform, but that doesn't mean it always refers to the horizontal surface. Some kinds of movable rostrum have a permanently or semi-permanently attached lectern, railing, or other such pieces that extend above the floor surface; a request to place something on the rostrum could be interpreted as either an instruction to spread the item on the floor, place it on the lectern, or hang it from the railing, depending upon the nature of the item in question.