Alright, I think I understand why I was confused. These are just my thoughts and totally not a very scientific analysis at all, but I think the problem is that not a single explanation for friction is sufficient.
The two main questions I want to answer:
- Why Static Friction is greater than Kinetic Friction
- Why friction only sometimes means adhesion
There isn't just a single cause for friction. Friction is just any force that opposes the force applied when two surfaces are in contact.
That being said, there are two main models showing why this happens. I think some of us learned one, and some of us learned the other (by us I mean students still only starting physics), so I'm just going to put the two together and hopefully, it helps paint a clearer picture.
The first depends on the "roughness" of the surface:
This is because, as @Ben51 described, if the two surfaces aren't smooth, parts of one "interlock" with parts of the other. Those interlocking parts must then be broken off the surfaces when we apply a force if we want the objects to slide past one another, and thus the applied force must be great enough to break them.
This explains why when we slide REALLY rough surfaces past each other, we see little pieces flying off the surfaces. Those are those interlocked parts being broken.
However, this doesn't answer my questions. For one, why is it that static friction is greater than kinetic friction? Secondly, if you look at a table of roughness VS friction, why is it that once surfaces start getting really smooth, friction starts increasing?
If friction was only caused by the two rough surfaces interlocking together, those "microscopic ridges" would need to be broken regardless of whether the two rough surfaces are sliding on one another, or they aren't.
Saying that we don't need as much of a force to accelerate an object once it has started sliding because the relative velocity of the surfaces itself helps break the interlocked parts off isn't really a valid explanation.
Breaking those parts requires the same exact amount of force regardless of whether the surfaces are moving or not. Each break will take the same amount of momentum away from the moving surfaces as it would from the momentum given to the stationary one. And as long as the normal force doesn't change, there isn't really any reason for there to be more or less interlocking ridges once the objects start moving relative to one another.
To really explain why static friction is greater, we need to then use a different cause for friction: small intermolecular bonds forming between the two surfaces.
I think static friction is greater than kinetic friction because of this exactly: when the two surfaces start off relatively still to one another, not only must the ridges be broken, but we must also overcome weak bonds between the two surfaces! These don't form when the objects are in relative motion because as one surface slides over the other, there isn't time to form them!
This is also the reason why hyper-smooth surfaces experience so much friction! Since there are almost no rough parts causing a separation between the atoms of one surface and the atoms of the other, the surfaces stick together a lot more (search up cold welding).
I think friction caused THIS way will also cause adhesion, and is, in fact, responsible for the adhesion between any two surfaces, simply not on a noticeable scale because most surfaces aren't smooth enough. And to answer my original question, the force of static friction is greater than adhesion on everyday surfaces because static friction takes into account the bonds AND the ridges, while adhesion only takes into account the bonds.
(I've read other explanations, one said that a vacuum formed between smooth surfaces pressed together and pulled them closer, another that a layer of water held smooth surfaces together, but this is the only explanation that isn't dependent on external agents being the cause)
For the wheel rolling without slipping (at a constant velocity), when the little atom on the circumference of the wheel touches the ground, it never feels a lot of friction because it doesn't need to break any ridges on the ground. This is because its motion relative to the ground looks like this:
It touches the ground almost vertically, so it wouldn't NEED to break any ridges. The only connection it will feel to the ground is an insignificant amount of adhesion, caused by a small attraction to some atoms in the ground.
However, when we try to accelerate the wheel, the ridges DO come into play, and its the ridges and not intermolecular bonding which causes a net torque on the wheel!
I guess the only way to test this theory (that the intermolecular forces cause adhesion and a greater static friction than kinetic friction, but they aren't as prevalent once the objects start sliding relative to one another) is to see if adhesion forces are reduced when two surfaces are in relative motion with one another. Or to get a microscope and see if a small separation appears between two surfaces once they start moving relative to one another since inter-surface bonds aren't holding them together as tightly.
However, since most everyday surfaces are too rough for this to be prevalent, we don't usually notice it!
Again, these are only my thoughts and not a scientific explanation at all, but hopefully, by putting the two concepts together, this helps someone curious on the internet. It definitely helped me.