We only refer to MSA when talking about Arabic. Most Arab speakers consider dialects side languages to Classical Arabic. They have never had a transcription throughoutout history. People started writing in their dialects only recently with the arrival of SMS and the internet.
I get that as a new comer to Arabic you probably have come across learning materials for dialects like Egyptian and levantine. But in reality you won't find uni courses for those dialects because academics don't consider them to be proper languages with clear grammar and an established vocabulary.