The SRD for improved grab states (emphasis mine):
If a creature with this special attack hits with a melee weapon (usually a claw or bite attack), it deals normal damage and attempts to start a grapple as a free action without provoking an attack of opportunity. No initial touch attack is required.
Unless otherwise noted, improved grab works only against opponents at least one size category smaller than the creature. The creature has the option to conduct the grapple normally, or simply use the part of its body it used in the improved grab to hold the opponent. If it chooses to do the latter, it takes a –20 penalty on grapple checks, but is not considered grappled itself; the creature does not lose its Dexterity bonus to AC, still threatens an area, and can use its remaining attacks against other opponents.
A successful hold does not deal any extra damage unless the creature also has the constrict special attack. If the creature does not constrict, each successful grapple check it makes during successive rounds automatically deals the damage indicated for the attack that established the hold. Otherwise, it deals constriction damage as well (the amount is given in the creature’s descriptive text).
When a creature gets a hold after an improved grab attack, it pulls the opponent into its space. This act does not provoke attacks of opportunity. It can even move (possibly carrying away the opponent), provided it can drag the opponent’s weight.
The regular rules for grappling, state (emphasis mine):
Damage Your Opponent: While grappling, you can deal damage to your opponent equivalent to an unarmed strike. Make an opposed grapple check in place of an attack. If you win, you deal nonlethal damage as normal for your unarmed strike (1d3 points for Medium attackers or 1d2 points for Small attackers, plus Strength modifiers). If you want to deal lethal damage, you take a –4 penalty on your grapple check. Exception: Monks deal more damage on an unarmed strike than other characters, and the damage is lethal. However, they can choose to deal their damage as nonlethal damage when grappling without taking the usual –4 penalty for changing lethal damage to nonlethal damage (see Dealing Nonlethal Damage, page 146).
I can see two possible readings for a character that has Improved Grab, an optimistic and a more 'realistic' one.
Reading 1 (Optimistic):
- Character goes for the option damage your opponent, he makes a grapple check and succeeds.
- The character deals unarmed strike damage per regular grapple rules.
- The character also does natural attack damage (and possibly constrict damage) because a successful grapple check was made.
Reading 2 (Realistic)
- Character goes for the option damage your opponent, he makes a grapple check and succeeds.
- The character does natural attack damage (and possibly constrict) because improved grab replaces regular grapple rules (in regards to damaging your opponent).
The question therefore is, which of these readings is correct per RAW?