According to Encyclopaedia Brittanica, the quadrille is a dance performed by four couples in a square formation and features several intertwining figures.
The mazurka is best known as a Polish dance, and is often accompanied by bagpipes or the accordion, though some Russian composers also composed mazurkas for solo piano performance. The mazurka is a versatile dance, which can be performed by groups of 4 or 8 couples, or by a single couple, and while it is characterized by stamping feet and clicking heels, it is highly improvisatory. The mazurka features prominently in the ballets Swan Lake and Coppelia, as well as in several Russian novels, including Anna Karenina and War and Peace. An example from Coppelia is below.