Yeah I always assumed "bug" was like "vegetable" --- it's a colloquial, not taxonomic, term. But there are "true bugs" so maybe the analogy isn't completely sound.
They're culinary vegetables. My wife likes to say it like this: intelligence is knowing that a tomato is a fruit, wisdom is knowing that it doesn't go in a fruit salad.
You know you can just put whatever you want in your salsa right, no cop is gonna stop you. I have a very nice mango salsa the other night, it was only one step removed from a fancy fruit salad.
Bug is a technical term. Only insects of order Hemiptera, categorized by the ability to fly and the presence of piercing, sucking mouth parts, are considered true bugs.
I'm sorry but you're simply incorrect. Bug can be a technical term, but that doesn't also preclude it from also being a non-technical term, because words often have more than one meaning. See also: theory.
a: any of an order (Hemiptera and especially its suborder Heteroptera) of insects (such as an assassin bug or chinch bug) that have sucking mouthparts, forewings thickened at the base, and incomplete metamorphosis and are often economic pests
called also true bug
b: any of various small arthropods (such as a beetle or spider) resembling the true bugs
c: any of several insects (such as a head louse) commonly considered obnoxious
"a: any of an order (Hemiptera and especially its suborder Heteroptera) of insects (such as an assassin bug or chinch bug) that have sucking mouthparts, forewings thickened at the base, and incomplete metamorphosis and are often economic pests"
This is the primary and most correct definition of bug.
Yes, people use it wrong. That doesn't change the definition of the word.
The scientific taxonomic system was made, in part, because traditional colloquial terms are a mess. For example, "daddy longlegs" refers to a type of spider in my area, but there are two other animals and three plants that it could refer to depending on where you grew up. Taxonomists saw that there are ten different standards, decided to make a new one to replace them all, and for once, it actually worked out for the most part.
"Bug" is one of those old terms. It might have been mapped post hoc on top of the modern taxonomic system, but it didn't start that way, and isn't always used that way. I wouldn't expect an entomologist to use the term at all in formal contexts.