How does the taxonomy go?
First, they're arthropods, in the same phylum as the insects: they have a segmented body, paired appendages, an exoskeleton, and they molt.
Next level down, cutting out the insects, Subphylum Crustacea. Antennae, gills, five segments, five pairs of appendages. A carapace. This covers a raft of critters, from barnacles to lobsters, some 42,000 species.
Below Subphylum is Class; now we're in Malacostraca. Head, thorax, abdomen; appendages everywhere. 18,000 species. Crabs, lobsters, shrimps, isopods, krill (what whales eat). Hermits fitting in nicely.
Superorder Eucarida. Head and thorax fused into the cephalothorax. Eyes on stalks.
Order Decapoda, which means "Ten feet". These include the pincers (chelipeds); besides that, there are the two stalked eyes, two pairs of antennae (yes, the crabs have them, too, but they're small.), and three sets of mouthparts. We're down to 10,000 species. Still the shrimps, lobsters, crabs.
And here's where the split comes, at the Superfamily level. There are "true" crabs, the Brachyura, and "false" crabs, the Paguroidea or hermits, plus a few others. The "true"crabs have a short, flat body, with the abdomen reduced to a flap folded over the reproductive organs. There are about 4,500 species.
The Paguroidea make up another 500 species. These are the "false" crabs.* Maybe I'd prefer to call them the "true"hermits; they're at least as honest as the flatties. Except for their habit of stealing other critters' housing.
Crab carapace. Dungeness crab, Cancer magister. Discarded home, but useless for hermits.
Ok, I think I've got that sorted out. I'll go on to more crab stuff tomorrow.
*Update; Tim notes, in the comments, that the hermits have only 6 walking legs. They're still decapods ("ten feet"), but the last two pair are reduced to hooks that hold the shell they borrow. So it's: first pair, pincers (chelipeds); second, regular leg with claw; third, no claw; fourth and fifth, shell hooks. In "true" crabs, it's: first pair, pincers; second to fourth, walking legs; fifth leg, swimming leg.