Courtesan, in modern usage, is a euphemism for a kept mistress or prostitute, particularly one with wealthy, powerful, or influential clients. The term historically also referred to a courtier, a person who attended the court of a monarch or other powerful person.
Veronica Franco, famous Venetian poet and courtesan. Portrait by Paolo Veronese.
Courtesans with their servants by Lancelot Volders
Olympe Pélissier (Vernet, 1830) was described by Balzac as "the most beautiful courtesan in Paris". In 1846, she married Rossini.
Lais of Corinth by Hans Holbein the Younger, Kunstmuseum Basel
A mistress is a woman who is in a relatively long-term sexual and romantic relationship with someone who is married to a different person.
Madame de Pompadour, mistress of Louis XV of France, c. 1756
Eugène Delacroix's c. 1825 painting Louis d'Orléans Showing His Mistress
Domitila de Castro, long-term mistress of Emperor Pedro I of Brazil