Question

a sponge and a bar of soap occupy the same amount of space, but the soap is much more dense than the sponge

Answer 1

The sponge floats whereas the soap falls. The particles in the soap are tightly packed so it sinks straight to the bottom, the insides of a soap are also NOT hollow therefore it does not float. A sponge can tale in water while still having air pockets which make it float. As you can see, a sponge is also lighter than a soap.

Answer 2

Yes, that's correct.  That's a big part of the reason why
the soap floats in water and the sponge sinks in it.