As evidenced by the other answers posted to this question, the difference between novels and drama will depend on how we are using the terms.
Drama, as a formal literary term, describes the form of writing used for the theater. All plays are drama in the most literary, formal usage of the term. When drama is used this way, it is often phrased as dramatic form.
This terminology helps to avoid a confusion that stems from the fact that within the realm of theatrical writing there is a common, categorical distinction between plays. There are dramas and there are comedies.
The word is taken directly from the Greek drama, meaning “a deed or action of the stage.” The Greek word evolved from the Greek term dran, meaning “to do” or “to act” (eNotes).
In this sense, a drama will be a play that features a narrative which "dramatizes" the human experience in one way or another. Here "dramatize" means "bring to life" or "show via exaggeration." (It is this last meaning of the term drama that relates most closely to the everyday use of the phrase as it turns up in conversation.)
"Novel - a lengthy fictitious prose narrative portraying characters and presenting an organized series of events and settings" (eNotes).
The novel is a form of fiction writing that features prose as its central element and which offers a narrative (or set of narratives) with a beginning, middle and end. Longer than short stories but the same in terms of its reliance on prose writing, the novel is a very flexible mode of writing that has been used in various ways to tell stories since Don Quixote of La Mancha was published in 17th century Spain.