The term studio recording means any recording made in a studio, as opposed to a live recording, which is usually made in a concert venue or a theatre, with an audience attending the performance.
In the case of Broadway musicals, the term studio cast recording applies to a recording of the show which does not feature the cast of either a stage production or film version of the show.
The practice has existed since before the advent of Broadway cast albums in 1943. That year the songs from Rodgers and Hammerstein's Oklahoma!, performed by the show's cast, were released on a multi-record 78-RPM album by American Decca. (London original cast albums have existed since the early days of recording, however, and there are recordings in existence of excerpts from such shows as The Desert Song, Sunny, and Show Boat, all performed by their original London stage casts.)
Before 1943, musicals were recorded in the U.S. with what might be termed studio casts, although in many cases, such as those of Walter Huston from Knickerbocker Holiday and Helen Morgan from Show Boat, singer-actors from a musical did make recordings of songs from the shows they appeared in. Another such example is Ethel Merman, who recorded virtually all of the songs that she made famous, even when there was no original Broadway cast album of a smash hit that she had starred in, as is the case with Girl Crazy, Panama Hattie, and Anything Goes. Paul Robeson, who appeared in several productions of Show Boat (though not the original Broadway production), made many recordings of the song Ol' Man River from the show.