not exactly. they are both comprised of silicates, but diatomaceous earth is much finer. diatomaceous earth is almost like brown algae that has build up over years and formed a layer on the bottom of a lake/ocean etc. pool filter sand is just that: sand.
Right, Diatomaceous earth is very, very fine shells etc, like powder. Pool sand is larger uniform sized particles that can be vacuumed by all but the strongest gravel vac with very little getting sucked up.