From the 3.5 SRD:
IMPROVED GRAPPLE [GENERAL]
Prerequisites: Dex 13, Improved Unarmed Strike.
Benefit: You do not provoke an attack of opportunity when you make a touch attack to start a grapple. You also gain a +4 bonus on all grapple checks, regardless of whether you started the grapple.
Normal: Without this feat, you provoke an attack of opportunity when you make a touch attack to start a grapple.
Special: A fighter may select Improved Grapple as one of his fighter bonus feats.
Improved Grab (Ex):
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.
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Okay, let's look at the differences.
Improved Grapple is a feat, with normal feat prerequisites (Dex 13, Improved Unarmed Strike). You cannot use the feat unless you have the prereqs or an item that bestows them. Further, it still requires an attack action to initiate a grapple - the only benefit of the feat is to eliminate the AoO allowed when making a normal grapple attempt.
Improved Grab, OTOH, is a creature ability found in the MM. It allows a creature to initiate a grapple as a free action whenever it hits with the appropriate appendage (claw, bite, tentacle, etc). Since it's not a feat, it also does not list prereqs. The one drawback is the standard requirement that it be used only against creatures at least one size category smaller.
As you can see, Improved Grab is superior to Improved Grapple in a number of ways. To use Improved Grapple, the character wielding the claw will have to have a Dex score of 13+ and the feat Improved Unarmed Strike. If the wielder lacks either of these (for instance, if he's taken ability damage to Dex), then he can't use Improved Grapple. Further, it still requires an attack action to initiate the grapple. It's not a free action.
From what you've said, it sounds like Improved Grab fits your concept better. Unfortunately, no GM in his right mind is going to allow it. I'd consider allowing Improved Grapple (and even Improved Unarmed Strike) with the weapon, but it would be costly to have both feats - and your character will still have to meet the Dex requirement.
Finally, see the highlighted passage under Improved Grab for an explanation of the -20 grapple penalty others have referred to. It's critically important when facing enemies who can take advantage of an opponent who's lost his Dex bonus, e.g., rogues. Otherwise, it's probably not a big deal. Unless your character will have significant bonuses to his grapple checks, I doubt you'll choose to take the -20 penalty.
