Can all phrases that are considered idioms sometimes fall under the category of slang? Are they under the colloquial category because of everyday use?

(This is not a duplicate anymore because I edited my question, please read all the information in this body and in all of the comments there are 10 comments so far)

After reading about the difference among informal, colloquial, slang, and vulgar (What's the difference between "informal", "colloquial", "slang", and "vulgar"?), I noticed there was no mention of idiom. Idiom, I would think, falls under the category of colloquial, but this site (https://www.askdifference.com/colloquialism-vs-idiom/#) says there is a difference and I’m having a lot of trouble seeing it because on that site an idiom "is a phrase or an expression that has a figurative, or sometimes literal, meaning. Categorized as formulaic language, an idiom’s figurative meaning is different from the literal meaning." and on that same site colloquial is "Everyday language, everyday speech, common parlance, informal language,…" and according two these two definitions it looks like idiom can fall under the category of colloquial because colloquial is "Everyday language, everyday speech,…" With that being said, why doesn’t this site just say that idiom falls under the category of colloquial? Would idiom ever fall under the category of slang? If so, please give examples.

(Edit)
In addition:

Here are some examples of phrases that are considered idioms to think about:

• It’s a piece of cake
• It’s raining cats and dogs
• There are other fish in the sea

There is more where that came from. The site I found these idioms was this one: https://www.ef.edu/english-resources/english-idioms/

If you have better examples to think about, please include them in your answer.

(Note: Does anyone know if my question can be reopened? I edited my question. It used to say: Does idiom fall under the category of slang or does idiom only fall under the category of colloquial? I edited it to say: Can all phrases that are considered idioms sometimes fall under the category of slang? Are they under the colloquial category because of everyday use? And because of the my clarification in the comments that led to my edit, my question should no longer be considered a duplicate. Please Help!)