I had a "oh now I get it" moment after doing a bunch of research and testing on wheel settings in career mode, and here's my attempt at the post that would've saved me some time:
Friction Control: Varies the amount of friction between the wheels and the ground. You can think of this as changing out different sets of tires with varying amounts of grip.
Higher Friction Control: The wheel is less prone to sliding, slipping, and spinning out, at a tradeoff of the craft being more likely to flip over during a turn (the wheel becomes more likely to lift off the ground when rapidly changing direction since it doesn't want to skid). Higher friction can help keep a vehicle in place when braked on an incline. It can also help keep wheels from spinning out in low gravity environments (lower gravity = less downward pressure on the wheel, for which higher FC can help compensate).
Lower Friction Control: The wheel is more likely to slide, both front to back and side to side, and hence a craft with low FC may be more likely to spin out than to flip over. It can also make your steering-enabled wheels less responsive (they slide a little in addition to turning), which helps keep a rover stable at high speeds by preventing overly tight turns. Wheels with lower FC are less responsive to acceleration and braking as well.
Having a higher friction control on the back wheels (with steering disabled) can prevent you from spinning out
Having a lower friction control on the front wheels (with steering enabled on the front and not the back) can prevent you from flipping over while trying to steer at high speed (effectively makes your wheels less responsive to steering without enabling advanced tweakables)
You may need higher friction control when driving up and down steep inclines or on low gravity surfaces
Consider combining tweaks to brake percentage with tweaks to friction control when trying to keep your planes from spinning as you land/brake
More of a brakes thing, but remember that KSP doesn't have anti-lock brakes, so if you're spinning out while breaking try pumping the breaks rather than holding them down
Traction Control: Lowers the motor output to a wheel if it is spinning faster than the vehicle is moving. It's like the traction control in cars. The Drive Limiter function lets you lower the amount of power the motor is outputting to the wheels
Higher Traction Control: The motor will put out less torque as a wheel meets/exceeds the vehicle's speed. This can prevent a wheel from spinning out (no torque for you until you match the rest of the vehicle!), but tends to lower motor output for the wheel overall. This lower output can also use less electricity per wheel on average when traveling.
Lower Traction Control: The motor will continue to provide higher output as the wheel approaches/exceeds the vehicle's speed. This can make a wheel more prone to spinning out (overcoming its friction with the ground and sending your rover flying out of control). Lower traction control can help a vehicle on steep inclines (as it delivers more power to the wheels) or if a vehicle is stuck.
Pay attention to electricity resource consumption and the "Motor" status gauges in the wheel right click menu to get a better sense of what Traction Control is doing to your vehicle
Unlike Friction Control, Traction Control only affects your vehicle if you're using the motor. If you're powering your vehicle with jets, rockets, or rotor blades, Traction Control isn't relevant
Dev Blog References here, here and here
Hope this helps, and if I missed something important/got something wrong, please chime in!