ATF in 2010 sent out training to FFLs that clarifies the pistol grip shotgun issue. Originally they were treated as pistols by the ATF, at least the inspectors at the San Antonio branch. (That's also an issue ... 20 answers from 20 people). However now they are classified as "other" and must be written down as a "pistol grip firearm".
The pistol grip shotguns are "others" unless the OAL is under 26" (measured with stock extended) and the barrel is 18" or greater, measured with the action closed and a dowel road inserted until it hits the bolt face; from the bolt face to the end of any permanently attached devices (including suppressors / flash hiders / etc.).
If you retain the pistol grip and the length or barrel is reduced below the above limits the gun becomes an "AOW". It is essentially a smooth-bore pistol at that point. Manufacture of an AOW costs $200 (stamp), but transfer of an AOW is $5 (stamp). A properly licensed manufacturer can apply for a taxless manufacture to convert your shotgun into an AOW, and then charge you $5 for the transfer stamp. You cannot put a stock on an AOW registered shotgun, as it then becomes an SBS.
If you stock the shotgun or it has a stock on it and the barrel is under 18" then it becomes an SBS (Short Barrel Shotgun). That's a $200 manufacture stamp.
Question here was the definition under State law.