We say that growth and differentiation in plants is open and not so in animals despite both growing is because the plant growth and differentiation of certain parts like the meristematic tissues of the meristems present in different locations of the plant body is an active site of cell division where growth is indefinite. The cells keep on dividing at the meristems and hence growth occurs indefinitely. Because new cells are constantly added to the body of the plant it is called open growth.

Yes, this statement shall hold true for sponges as well.