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.