As Ron suggested, common names can be deceiving and localized. But he did good in trying to answer your question.
I haven't used factory wood for many years, started whittling my own and then buying custom well over 25 years ago. Since I had very little interest in their wood I don't remember for sure just how many versions or variations there really has been, and there was more versions of forends than grips. I got my first Contender in 1968/69 and have had a bunch of them since, so I probably have also had just about every version of factory wood they ever offered even though I didn't use it. That said I'll toss a few ideas out here, but this old brain may not really remember what is right for sure.
I too refer to the top picture as being the Herrett style because they are what came on the limited edition Steve Herrett Commemorative Contenders. But I am certain that they had at least 3 different black plastic end caps that came on the grip... an elongated & checkered 2 screw diamond and a stylized octagon 3 screw that did not cover the bottom of the grip, and a full size 2-screw oval cap that almost did. Forends were offered in at least 3 versions too... one for octagon barrels with one screw, one for bull barrels with one screw and one for "Super" barrels with 2 screws. Remember these sets the best because of all the factory wood offered this is the version I used the most (other than before I made my own or bought custom) and I bought several sets of them over the years.
Second picture is one that had more than one version. Differences I remember were in the checkering footprint, the grip caps and the forends. Seems like some had black plastic caps with a raised "TC" on them, some the silver metal cap with a raised rim & cougar head and some had a silver metal cap with a raised rim, TC in a circle and an oblong plaque with a black anodized background. Forends were either snap on or screw mounted, they also had checkering variations and with the screw mounted either with or without a ducktailed tip. These forends may have been for more than one grip style too.
Last picture with the rubber insert I sure want to call the Competitor grip, but I am not certain that's right. I agree it was the last grip style offered for the Classic frame though.
I agree with Ron too that the first factory wood was very square. I never had a problem with them on the factory octagon barrels being offered, but luckily at that time no boomer wildcat barrels had yet been devised for the Contender. It was not a comfortable grip.
Note: I don't remember where this fits into the sequence, but here is another grip they offered. The end of the butt has a curved tear drop shaped profile, and so a metal cap with raised edge and cougar head that was also that shape. Might have been other cap versions for it too?
I also remember other forend styles different than all of the above, but not what grip they went with for sure. I recently sold off a bunch of both factory and custom Contender wood, so too late now for pictures. I think all I have left in factory wood now is a Herrett grip with a matching 10" octagon barrel forend, and an early snap on forend (complete with ball screw) that is also for octagon barrels. Oh well....
All just from memory, so most definitely all open for correction. HTH
L.