Yes, the difference is that instead of it being firm or soft depending on if you use cold or hot water (respectively), it has a firm side and a soft side that remains that way regardless of water temperature.
At least, that's my understanding, I've never tried a scrub mommy
Realistically, I prefer having a scrub daddy and a separate sponge. Cuz the scrub daddy’s plastic mesh lasts a long time and doesn’t trap food particles, but sponges trap food and get gross really quickly. I’ve found that I end up replacing a scrub mommy way more often than a scrub daddy, simply because the sponge side is gross. It feels wasteful, when I could simply have a separate sponge that I replace as needed.