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The question here is really about FK (forward kinematic) versus IK (inverse kinematic) rigging; a lot of SFM users confuse "rigging" and "IK rigging".
Anyway, Forward Kinematics is where you use the rotations of joints to determine the final position of the end of a bone chain. (In this case, the end might be the hand, and the bone chain the arm).
Inverse Kinematics is where you use a desired final position of the end of the chain to determine the necessary joint rotations to achieve it.
They both have their merits, but for most animation, you're generally going to be more concerned about having the character's hand in a specific place than having their elbow articulated at a specific angle, and so IK is generally easier.
Say, for example, you want to have a character push a briefcase full of money across a table - you want their hands to be moving with the briefcase.
Doing that with Forward Kinematics would be a right pain in the bum; you'd almost have to position the wrists, elbows and shoulders correctly frame by frame. And then if you later decide you need to change exactly where they've pushed the briefcase to, it would all have to be done again.
With IK though? Just tell the computer that the hands move from here to here, and it'll do all the calculation of the shoulders, elbows and wrists for you.
FK can be better for sweeping arm movements like throwing a ball (where the hand doesn't have to have an exact position to match the scenery), but IK can also be used fairly well here, so most people will just stick to IK, particularly given that SFM doesn't switch well between the two.
(Although it is possible to build rig scripts that provide a mix of IK and FK support, a lot of people don't bother).
I will add that models have to be built by default on Forward Kinematic rigging. The maths of Inverse Kinematics needs an FK skeleton to exist so it has the information about the shape of the model.
TL;DR There are two kinds of rigging. The first is the basic skeleton. When you use SFM, you would recognize the skeleton when you select the whole model. It allows for control over an area the bone is responsible for, not limited to rotation and translation, or posing in SFM sense. You can have just a rootTransform and be able to pose the model, but it is more fun when the model has more bones so that you can do more interesting things with it.
IK Rigging is a system that does animations for you essentially. I always considered it to be the same as things like jigglebones because it is pretty much the equivalent of activating a preprogrammed system that will control the posing based on the bone selected and oriented, as well as the calculation of certain "collisions," like the floor, which I think it relies on rootTransform rather than the actual floor in the map. That is all you really need to know about IKs. Only when they are turned on do they work as intended.
Non-rigged models will automatically have the rootTransform bone, and they are mainly designed to exist as props and minimally animated components. All you can do is pose them at certain parts. Some props don't have rootTransform lined up with themselves, and this could either be because they have another root bone and were posed so that they could be compiled correctly in Hammer (Map Making program), or they were modelled this way as a non-interactive prop.