The term romance (Spanish: romance/romanza, Italian: romanza, German: Romanze, French: romance, Russian: романс, Portuguese: romance, Romanian: romanţă) has a centuries-long history. Applied to narrative ballads in Spain, it came to be used by the 18th century for simple lyrical pieces not only for voice, but also for instruments alone. The Oxford Dictionary of Music states that "generally it implies a specially personal or tender quality".
Instrumental music bearing the title "Romance"
Typically, a Classical piece or movement called a "Romance" is in three, meaning three beats in the bar.
Amy Beach: Romance in A major, Op. 23, for violin and piano
Romance in E major for cello and piano, from Suite for Cello and Piano Op. 16 (1862), later published as Op. 67 in 1866 as a standalone work for horn or cello and piano
Romance in F major for horn (or cello) and orchestra, Op. 36 (1874)
Mozart subtitled the second movement of his piano concerto no. 20 in D minor (K.466) "Romanze" and the second movement of his third horn concerto "Romance".
D 114, "Romanze" ['Ein Fräulein klagt’ im finstern Turm'] for voice and piano (1814; 2 versions)
D 144, "Romanze" ['In der Väter Hallen ruhte'] for voice and piano (1816, sketch)
D 222, "Lieb Minna" ['Schwüler Hauch weht mir herüber'] for voice and piano (1815, also appears as "Lieb Minna. Romanze")
D 907, "Romanze des Richard Löwenherz" ['Großer Taten tat der Ritter fern im heiligen Lande viel'] for voice and piano (1826?, two versions, 2nd version is Op. 86)
So many composers in the French tradition wrote Romances sans paroles, "Romances without words", from the 1840s onwards that the radical poet Paul Verlaine in turn published a collection of his impressionistic poems as Romances sans paroles (1874).
(in French) Henri Gougelot, La Romance française sous la Révolution et l'Empire: choix de textes musicaux (Melun:Legrand & Fils, 1937) [2nd ed., 1943]
(in French) Henri Gougelot, Catalogue des romances françaises parues sous la Révolution et l'Empire, les recueils de romances (Melun:Legrand & Fils, 1937)