Information from the OED on some similar terms. Some of the quotations are rather interesting!
Sing-song: An amateur concert of an informal nature; a convivial meeting where each person is expected to contribute a song. Early citations: "The dinner o'er, the sing-song done" (1769, Trinculo's Trip); "The wealthy [have] their 'ancient concerts' the costermongers what they term their sing-song" (1857, Night Side London); "Sing-Song, a choral meeting at a pot-house" (1865, Slang Dict.)
Sing-along: A sing-song to the accompaniment of a song-leader or tune. Early citations: "There would be a sing-along, or the manager maybe would just pull a lucky number from a hat" (1973, Ten Lost Years); "The insulting notion that working-class audiences want only a beery community sing-along on their night out" (1979, The Guardian).