Is "moving into the defender's space" analagous with "moving out of a threatened square"?

Question

There are two special attacks that call out "moving into the defender's space"; bull rush and overrun.

In the bull rush description, under Initiating a Bull Rush,

First, you move into the defender’s space. Doing this provokes an attack of opportunity from each opponent that threatens you, including the defender. (If you have the Improved Bull Rush feat, you don’t provoke an attack of opportunity from the defender.)

While not explicitly stated, this does seem to imply the provocation is from moving out of a threatened square, since the result would be the same if it was worded as the following.

First, you move into the defender’s space. As you are moving out of a threatened square, this provokes an attack of opportunity from each opponent that threatens you, including the defender. (If you have the Improved Bull Rush feat, you don’t provoke an attack of opportunity from the defender.)

However, the wording in overrun is much more terse.

Since you begin the overrun by moving into the defender’s space, you provoke an attack of opportunity from the defender.

There's nothing about Improved Overrun or about provoking from other opponents in this step, and the feat mentions nothing of not provoking. To further obscure matters, the table for standard actions in the combat section indicates an overrun does not provoke.

The rules-as-intended are unclear to me. How would you recommend ruling this at the table, to be at least as close to rules-as-written?

I've considered a house rule; to treat "moving into a defender's space" as "moving out of a threatened square", and assume bull rush and overrun provoke in the same manner. To complete the house rule, it would probably be good to drop the awkward "the target may not choose to avoid you" from Improved Overrun and replace it with "you do not provoke an attack of opportunity from the defender".

Is there something I'm missing here, and perhaps "moving into" is not (intended to be?) the same as "moving out of"? Are both the table and the specific description correct, in that an overrurn is intended to provoke only from the defender? I mean, overrun does not call out specifically not provoking from movement, so I don't see why the general rule would not apply?

Answer 1

Bull Rush is just being more explicit and covering more bases in its explanation, whereas Overrun is not bothering to re-quote other parts of the rules at you. They both work the same way.

When performing a bull rush or an overrun, or a charge, or whatever it is you're doing, if you move out of a square that a defender threatens, they are eligible for an AoO (if they have one left, etc etc.).

You are right that it's not "moving into a their square" that generates the AoO per se, it's just moving out of another threatened square. Which provokes from not just the person defending against the maneuver but anyone else who's otherwise eligible. It's worded a little sloppily and making some assumptions, but in both cases they do explicitly link it back to the normal threatened area/AoO rules.