To understand what kind of comedy She Stoops to Conquer is, we first need to understand the two definitions of comedy. For most of us today, a comic work is one that is humorous. If we see a movie advertised as a "comedy," we expect to go to the movie theater and laugh at the antics of the characters. However, traditionally, and more broadly, a comedy is any work of literature that does not end with dead or disabled bodies. If the main characters are alive at the end, even after grim encounters with death, the piece is deemed comic. This why a play like Shakespeare's Measure for Measure is often called a "dark" comedy: everyone ends up alive, but only after brushes with death that bring to attention the cold and corrupt side of human nature.
When She Stoops to Conquer was written, sentimental comedies dominated the London stage. These were comedies in the second and broader meaning of the term: everyone was alive at end, but there wasn't much laughter. These plays, instead, tugged at the heart strings, perhaps by reuniting an impoverished mother with her long-lost son. As this play does not do this, it is considered an anti-sentimental comedy.
She Stoops to Conquer is often called a humorous or laughing comedy because Goldsmith wrote it to raise laughs. It is stuffed with jokes and absurd situations. As David Garrick wrote in the play's prologue, the "Comic muse, long sick, is now a-dying": Goldsmith with She Stoops to Conquer revives this form of play.
She Stoops to Conquer is also a comedy of manners, meaning it satirizes or pokes fun at upper-class pretensions, such as the exaggerated civility in which men treated upper-class women versus the bawdy way they treated lower-class women. It also pokes fun at Mrs. Hardcastle's pretensions of knowing London when she mixes up upper- and lower-class neighborhoods.