At first the piano playing mechanism was housed in a separate cabinet which was pushed up to the piano, hence the name "push-up player". In Germany it was called the Vorsetzer, literally, "sits before" the piano. Same idea.
But the cabinet was very heavy and care was needed not to break the delicate fingers which pushed on the keys. Once it was detached from the piano so that little Suzie could practice her lessons, the push-up player was likely to remain in the corner.
This web page is dedicated to advertising and illustrations of this forerunner of the player piano.