Wakaran or wakaranai? Am I correct in assuming that both terms mean do not understand or not understanding? Thanks.
Meaning: "I don't understand" (negative form of わかる)
Derivation: The speaker got lazy. It's a way to shorten the phrase to something you can say even faster. This form of speaking is most often associated with various dialects (方言).
Formality: This isn't formal. This is technically plain speech.
Meaning: "I don't understand." (negation of わかる)
Derivation: Plain form conjugation of わかる。 This follows typical conjugation rules, so nothing special here
Formality: Plain form. This isn't formal.
In informal situations usage of わからない／わからん is identical. Meaning is identical. The difference is that the speaker got lazy, and did not pronounce the 〜ない fully, resulting in 〜ん instead.
Personally, I reserved the use of わからん for people I had an established informal relationship with. This is because: 1) It's a slurred pronunciation, and so it's in my opinion a bit less formal than わからない、but not by much. 2) わからん is often associated with 方言、and for most of my working relationships, use of the local dialect was frowned upon, as it was considered less formal.