This question is related to another recent one, since I couldn't figure out the answer, even though I had all the resources.
Let's have an owlbear character that uses Improved Grab after successfully attacking with its claw.
Now, from SRD, 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.
Let's say that the Owlbear decides to use the second option and take a -20 to Grapple check and succeeds in establishing a hold.
The ability description says that the Owlbear is not considered grappled. Does that mean that the Owlbear is not grappling? There is a list of actions available for a character who is grappling Can the Owlbear select one of these actions or not?