"mei shi 没事" literally means "to have nothing to do" , it also means' It doesn't matter" "mei you wen ti没有问题" means "No problem". "out of problem".

"mei shi" means "It's nothing" whereas "mei you wen ti" means "No problem" . My chinese not very good. I just give a try.

"mei shi" has a mean of consolation. People say it to tell you "Do not worry". Sometimes it means "I can, but have a little trouble, but I do not want you to konw my trouble". Sometimes it means "be weary of, reluctant to discuss the matter". Please pay attention to the tone. "mei you wen ti" means "It is OK", "I can do it". The self-confidence of the man who said"mei you wen ti" is more. He wants you to trust him. Sorry for my English.If you have more questions, contact me.

"mei shi"mean isn`t,"mei you wen ti"mean "i can do it" or "there is nothing i want to ask"