although both wakaranai and wakarimasen means i don't understand, 'wakaranai' or wakaranai desu yo!' is used between friends as it is casual not formal.it the yo in the end represents the frustration of not understanding whereas 'wakarimasen' is a formal expression which can be use will talking to teachers or some one of a high status/age and strangers. wakarimasen is used with desta if you are saying it as a reply to what has been said before. so if someone said something and you don't understand it, you say."gomenasai demo, wakarimasen deshta, mo ichi do itte kurasai" which means "i am sorry but i didn't understand what you said, please repeat it one more time". hope this helped.

I don't know in japanese is "shirinai" in informal way and the formal way is shirimasen. I don't understand in japanese is "wakaranai" in informal way and the formal way is "wakarimasen".

both wakaranai and wakarimasen mean "i don't understand". do you know Honorific （keigo）? wakarimasen is more polite than wakaranai.

They are both the same.

No, it's just polite or not.