Some legal beagle will probably correct me but I think the fundamental difference is that a bomb goes bnag when it hits the ground (OK plus any delay, minus any proximity fusing, penetration etc) and a mine sits there all beligerent waiting for someone or something to pass nearby and hence set it off.
Mines can be 'sown' by air either in the sea or on land. Oh and they're illegal (well land mines are - not sure about marine mines) which bombs by and large aren't.
Some of our more cunning bombs were partly mines (JP 233) and so we've had to stop using them. Hug that tree - wear those open toed sandals with pride!