What kind of organisms can be covered by 益虫, 害虫 or 虫?

Question

I came across someone describing a Nihon yamori / gekko as a 益虫, and using "useful insect" in English. Gekkos aren't insects, but it made me curious what it actually does mean.

jisho.org only describes 益虫 as meaning "useful insect". The English edition of Wiktionary lacks a description of 益虫, has a terse description of its antonym 害虫 (harmful insect), and a slightly longer definition of 虫, but not one that'd cover gekkos.

What kind of organisms would be covered by 益虫, 害虫, or 虫, and what kind of animals wouldn't be covered by 虫?

(BTW: I'm aware that English has words for non-monophyletic groups, so no mockery is intended)

Answer 1

The Japanese Wikipedia has an entry for 益虫 which links to the English Beneficial insects, while 害虫 links to Pest.

However, unlike the English term it does look like 益虫 include not only insects (昆虫) but also other small animals:

益虫（えきちゅう、英: Beneficial insects）とは、何らかの形で人間の生活に役に立つ、昆虫など小動物のことを指していう言葉である。

"Beneficial insects(?)" refers the the various small animals, such as insects, which benefit human activities in different ways.

I guess geckos count because they are insectivores. The article itself gives カブトエビ (tadpole shrimp), which is no insect, as an example.

As for 虫, the Wikipedia states:

日本語の虫（むし）の概念は時代や個人による差もあるが、今日では主に水中以外の節足動物を指し、広義には獣・鳥・魚類以外の小動物全般を指す。

My attempt at translation (I'm not too certain about some terms):

The Japanese word "mushi" had different meanings depending on the historical period or point of view, but in modern times mainly refers to arthropods (except those living underwater). More generally, it can be applied to all small animals except mammals(?), birds and fish.

The article goes into more detail and seems to be pretty informative.