What's the difference between a novel and a drama?

Most plays and movies are enacted as if they are happening in the present. The scripts are almost invariably written in the present tense. Novels and short stories are usually written in the past tense. The first-person or third-person narrator is telling about something that happened in the past and is now all over with. Drama is effective because we see things happening right before our eyes. Novelists have the problem of writing about something that happened it the past but making the reader visualize the characters and events as if he or she is witnessing them in the present. Novelists can use many techniques that are not available to the dramatist. For example, a novelist can tell the reader what the various characters are thinking and can offer all sorts of information in the form of straight prose exposition. The dramatist usually has to have the characters convey information to the audience by talking to each other. We don't even know who these people on the stage are supposed to be until they address one another by their names. Much of the difference between drama and novels is that dramas show what is happening, while novels tell what happened. There are a few exceptions in both cases, no doubt, but they have never had a significant influence on the two different genres. Even when a play or movie attempts to deal with an event that occurred in the past, they have to depict the past as the present; and the script will describe everything in the present tense. Drama also has to be interpreted by actors and a director. The script is only the beginning of the project. Whereas the novelist as well as the short-story writer can handle the entire story alone.

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. 

Are there similarities between a novel and a drama?

These two forms of literature, the novel and drama, share a number of similarities. We may even argue that there are more similarities than differences in these forms. The most fundamental similarites shared by novels and dramata are the use of character and narrative. 

Though there are plays and novels that experiment with the boundaries of the form, eschewing many conventions, each will almost always feature multiple characters. The characters in novels and plays will usually be presented as real people with minds and emotions that allow them to make decisions within the context of the novel or play.

This is true even with fantasy novels that may use animals to stand in for people. The characters are real even there, insofar as they are understood to be capable of feeling and thought. They are not, in other words, mere symbols.

The second major similarity shared between novels and drama is the use of narrative. Both of these literary forms are essentially seeking to tell a story. Poetry and non-fiction do not share this element as a definitive trait. Though poetry and non-fiction can be used to tell a story, these forms do not necessitate a story as novels and plays do. 

Additionally, novels and plays are works of fiction, each might draw from a similar foundry of conventions (plot, symbolism, metaphor, irony, etc.) Each form can also be interpreted for theme and meaning in similar ways.