Trap blocking schemes generally involving blocking down (or inside) on the playside and puling an offensive lineman from the backside to trap or block the defensive lineman. Two advantages are that the playside lineman get the angle on their defender and you may be able to double team at the point of attack, and the trap can be an easy way to open up a hole if the defender is "getting upfield" to rush the passer as they want to do in today's game.
In zone blocking offensive lineman are generally stepping to their outside making the defensive lineman to their outside to react by stepping with them. At the point of attack you can get double teams on the lineman but as the linebackers flows to fill , the appropriate offensive line from the double team slides off and blocks the filling linebacker. OL stepping to the outside creates a stretch of the gaps and as the linebacker tries to read the back's path and fill it creates holes, the back initially steps to the point of attack and then is free to bang it through the hole, bounce to open areas in the outside or cutback as the linebacker pursues to the backs initial path. It is sorta like building a moving wall to one side and allowing the back to flow and then cut when a hole is created.
The backside end needs to be blocked by another back or read as in "zone read". The backside end is free because the Oline wall is moving away from him, so if he goes hard inside after the back the qb can read and keep it and run where the end vacated, or you can block the backside end in some way with another back /receiver to keep him from coming down hard on the back.
The good thing abut zone blocking is that the rules can be really simple and you can easily run it out of a one back four wide receiver set.