The 'zone' in zone defense is indicating that you are assigning each defender to a specific area of the court (or field) so the differences are in how you are splitting up the total area to be covered and how far a defender will need to move and where they will pass off their responsibility to a neighboring teammate.
In a 2-3 zone, the two guards each are responsible for half the court from around the foul line out, and the three forwards are patrolling from the free throw line in - sideline to edge of lane, lane, and edge of lane to sideline.
In a 3-2 zone, the three outer players are typically guarding three point line in the corner to edge of the free throw line, center free throw line extended and edge of free throw line to three point line in the corner, while the forwards are guarding two zones from the center line of the lane to out.
In attacking the various zone defenses there are two stresses an offense can create -
1. Players at the border between multiple zones - in just about every zone, the free throw line is the border of multiple different zones and whoever a defense uses to guard a player when they receive a pass there, leaves their zone empty of a defender.
2. Overloading a zone - for example having a player at the edge of a zone closest to the basket and another at the three point line - a single player cannot guard both players at the same time and one should get an open shot.
The disadvantage in zone defense is that it is very difficult to cover the three point arc completely so someone like KML is often referred to as a 'zone buster'. The advantage is that it tends to make dribble drives more difficult as the beating the outside defender just gets you into a new zone with a new defender waiting.