I would have guessed that slang had a slightly obscene (or at least coarse) nature and colloquialism was more an "informal convention of speech" without the negative connotation, but I can't find anything to back that assumption up.
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1britannica.com/topic/slang– Alex B.Jan 9, 2017 at 19:20
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'Slang' doesn't necessarily have a negative connotation IMO, but colloquial speech is much wider and covers sytnax, morphology, prosody, etc. In some languages, people even nasalise everything in colloquial speech.– WavesWashSandsJan 10, 2017 at 12:59
1 Answer
Slang is generally very informal language used a specific segment of speakers of a language. An example of slang (that I just found on the internet) is the word "Bandini", which is supposedly a word meaning "nonsense" used in Los Angeles.
Colloquial speech refers to everyday speech that people use informally. Colloquial speech can include a great deal of slang, or no slang at all. Colloquial speech is different from the standard of a language in that it has features like contractions (in English "can't" instead of "cannot"), more general words ("thing", "stuff", "dude"), etc.