un pouf (isn't it the same word in EN?) is a seat with a cushion but no legs.
solide , ( en bois) = a footrest , autrefois a footstool ( passé)
This is not the case in AE--for us a hassock is simply a specific type of this objet, as petit1 has explained above. (Of course, I guess it could be have a religious purpose, but that is not its exclusive meaning.)A hassock is specifically religious, and I think peculiarly Anglican. It's a hard cushion about 30x20x10 cm for kneeling on when praying.