Pride and Prejudice , similarly to the works of Oscar Wilde, George Bernard Shaw, and to a point Charles Dickens, is categorized as a "comedy of manners".
The "comedy of manners" is what we could consider in the 21st century as the equivalent of the romantic comedy, but it has specific qualities that makes the novel stand out from other types of social novels in that:
a. It uses witticism and sarcastic undertones to bring out the mannerisms and specific behaviors of the current societal memes. For example, the preocupations with social standing, marriage, the fashionable society, and being considered into the upper classes.
b. It questions the credibility of the most pompous character through exaggerating and basically satirizing them. Hence we have a Mrs Bennett and her rushing through getting her daughters married, and we often wonder how does this describe her as a good, christian woman.
c. In a comedy of manners there will be some form of love affair or ilicit affair going on which everyone might know about yet nobody mentions, or nobody knows but it is openly obvious.
d. The character in a comedy of manners do not challenge the characters that they openly satirize. The characters that are snobby, flippant, or arrogant remain the same, because (as manners require) you are to tolerate who is who in society, and your job (if you are below in echelon) is to be a mere observer--a witty and funny one at that.
The French term genre refers to a class or type of literature or art. Drama, Novel, Lyric & Epic are some of the basic genres. Each of these broad classes can be sub-divided, e.g. Tragedy & Comedy are types of the dramatic genre, whereas, Bildungsroman, Picaresque & Epistolary are some types of the genre of Novel.
Austen's novel, Pride and Prejudice, is a novel which may be called a novel of manners. Dwelling on the theme of marriage and set in a semi-rural society of the late 18th century, the book presents the life and manners of a select cross-section of people in the satirical light of a 'comedy of manners'.
Kathleen Morner and Ralph Rausch in NTC's Dictionary of Literary Terms define genre as "a type of any literary work". It is a French term. Abrams says that genre "denotes types or classes of literature". Which literary work would go after which genre depends on different criteria, and these criteria are highly variable (A Glossary of Literary Terms, M. H. Abrams).
Novels, poems, dramas- all are genres with their particular features. Pride and Prejudice is a novel. The novel is a lengthy fictional narrative in prose dealing with Characters, incidents, and settings that imitate those found in real life. (NTC's Dictionary of Literary Terms)
There are many types of novels: bildungsroman, Gothic novel, historical novel, romantic novel, social novel, satirical novel, psychological novel and so on. Pride and Prejudice have qualities of a satirical novel, a social novel and a romantic novel. Because of its themes, plot and characters, it becomes a romantic literary piece as well as a social novel having tastes of satire.