Please see the definitions:

- 忙 máng [adj/v] busy, very occupied; be busy, hurry

- 有事 yǒu shì [v] (of someone) be occupied or busy, have work (to do), have something (to do or deal with)

忙 refers to when someone is busy; 有事 means "have something to deal with".

We can use 有事 when someone has a request for others, for example - 我找你有事。(English: I need you for something I must deal with). This could imply that the speaker (I) needs to engage the listener (you) to deal with this matter.