"Slang" is slang for colloquialism

It depends a lot how you use both words. For me:

• colloquialism - anything you wouldn't use in a higher register of the language (e.g. when speaking with a judge, or when writing to a formal-ish audience)
• slang - colloquialisms allowed only in specific settings and associated primarily with a subculture

So one is a subset of the other. Some colloquialisms are not slang (e.g. EN gonna, tryna, wanna), but slang is always colloquialism (e.g. big dick energy, skibidi, bussy).

Note: that's how I use both words. But not even linguists agree on their definitions, so don't see yours as incorrect.

cute. a word that is itself