No. The classic common name is very misleading. Scientists and environmental educators are transitioning their language to seastar when referring to this animal because, well, it is not a fish.
The seastar is in the same family as the sea urchin, sea cucumber, sand 
dollar and a few others that all have these things in common: fivefold radial symmetry, spiny skin and a water based vascular system.
The family is called the “echinoderms” which means spiny skinned.
Image (c) dk clipart.
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A nice synopsis if you want more on echinoderms.