Man and gap and power is more a singular effort and zone is a group effort. In stretch zone the line runs laterally and shields guys off, the key is either forcing an overpursuit on the backside, or getting one guy to lose gap integrity, and then the rb hits the cut back lane and gets upfield, when you hear the term "one cut runner" they're referring to this sharp cutback.
Inside zone is a group effort from each half of the line, the line looks at the defenders on their side and has to put themselves in a position to shield off guys and get a sideways push, the goal is to open multiple gaps and getting a guy in the second level blocker, letting the rb take the best gap.
Man is a hat on a hat, gap is similar but targeted to one spot between 2 OL, say you're attacking the 2 gap against a 0 NT, the C will anchor the inside And push the nose to the right, while the LG takes the LB or DT and pushes them to the left, parting the defense.
Power is a gap concept, but involving pulling linemen and lead blockers to blast holes open, you often see the inside shoulder of the tackle targeted in power schemes, but dives are used often as well.