Both are forms of defamation. Generally, libel is written defamation, whereas slander is oral defamation.
Defamation is defined as the act of making an untrue statement (or statements) about another which damages his/her reputation. If the defamatory statement is printed or broadcast over the media it is libel, and if only oral, it is slander. In a practical sense, the difference in libel and slander is often simply whether there is some recorded version of the defamatory statement. If so, it could be construed as libel, even though it may be, for instance, a tape (or digital) recording of oral defamation. While a slander case might require witnesses to testify to the statement, a libel case typically only requires the recorded version of the statement itself.
Public figures, including officeholders and candidates, have to show that the defamation was made with malicious intent and was not just fair comment. Damages for slander may be limited to actual (special) damages unless there is malice. Some statements such as an accusation of having committed a crime, having a feared disease or being unable to perform one's occupation are called libel per se or slander per se and can more easily lead to large money awards in court and even punitive damage recovery by the person harmed.