In sha'Allah is used to show your approval on something. The closet translation for it in English is (God willing ) it means that everything will happen according to God's will
I also hear a slight nuance. Sometimes people say إن شاء الله when they are not sure about a future event or do not say overtly NO to an invitation they want to refuse. So they rely diplomatically on God. I hear then ممكن instead of إن شاء الله.
Mumkun is a more direct response. Insha Allah usually denotes that either the person is religious, which might not always be the case, or at least comes from a religious family or society where this expression is practiced.