No it is not, they belong to seperate familes as you can see by their scientific classifications
Sand Dollar:
Kingdom: Animalia
Phylum: Echinodermata
Class: Echinoidea
Order: Clypeasteroida
Suborder: Scutellina
Family: Mellitidae
Leske, 1778
Genus: Mellita
Sponge:
Kingdom: Animalia
Subkingdom: Parazoa
Phylum*: "Porifera"
Sand Dollar:
Kingdom: Animalia
Phylum: Echinodermata
Class: Echinoidea
Order: Clypeasteroida
Suborder: Scutellina
Family: Mellitidae
Leske, 1778
Genus: Mellita
Sponge:
Kingdom: Animalia
Subkingdom: Parazoa
Phylum*: "Porifera"
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No, they're both echinoderms but sand dollars are closer to sea urchins; they are essentially flattened sea urchins.