An “insect” or “bug” is an arthropod with six legs in the class Insecta. There’s also “true bugs” which are in the order Hemiptera (or even just the suborder Heteroptera if you are super nitpicky) - this includes things like leafhoppers, aphids, assassin bugs…

Within Insecta, we have Hemiptera, Hymenoptera (ants, bees, wasps), Coleoptera (beetles), Lepidoptera (butterflies, moths) and Odanata (dragonflies, damselflies).

To get to crabs, lobsters, and shrimp, you have to zoom out to jointed exoskeletons - Arthropods. (And I think crabs are a clusterfuck that make cladists cry, I’m in a landlocked state and haven’t got to do much ocean science myself so won’t put my foot in my mouth there.)

Other things that are “not bugs” but often called such - spiders, scorpions, whip scorpions and vinegaroons are all Arachnids (arthropods with specialized limbs called chalicerae - those cool things at the front of a spiders mouth), Rollie pollies/pill bugs are Isopods. Centipedes and millipedes are Myriapods.

Your larger point about how it’s weird that people get grossed out by the idea of eating mealworms but are okay with chowing down on shrimp is a good one though.