FM man-marking is only really man-marking as it is commonly understood when the OI instruction is chosen.
Man marking as a team or individual instruction to a player is actually more of a zonal man-marking. Whereas zonal is true zonal marking. This is because no-one really plays true man-marking tactics across an entire team any more. It just doesn't work in real life
Essentially the difference is that with zonal marking, your players will maintain the spacing and distance of your formation and mentality, whereas man-marking (in FM terms) will result in them covering and moving into covering positions more.
Rule of thumb is to put attackers on zonal and defenders on man-marking, with support players on zonal in attacking variants of your tactics and man marking in defensive variants.
Tight marking means that your player will get closer to whichever opposition is playing opposite to him or in his 'zone' of play. This means he can clear the ball before the opponent gets it or get in an early challenge but it also means that a ball over the top will leave him in a foot race if there is no cover and that a skillful and quick opposition player could potentially leave him for dead with a bit of skill or by knocking it past your player. As a general rule, it's good for pacey defenders who can recover from mistakes, or players who are dominant in the air or the tackle, not good at all for those players who need to be in space or who are liabilities in defence for whatever reason.
Closing down is a dangerous OI. It tells the nearest player/s to immediately try to get to the opposition player when he gets the ball. This works great when it's set for the opposition DMC - you don't want your attacking players man-marking him, because that just makes the DMC's job easier but you don't want the DMC to have time to set up attacks against you. But against an AMC this could mean that your central defence come charging out allowing him to play a simple through ball for a striker to score.
However, if you have the OI man-marking set up, then your nearest player will tend to be the one doing the man marking, and so closing down will usually only apply to him.
Hope that makes some confused kind of sense. Personally, I use a mix of both but would play full zonal with very, very top teams when attacking.