The slip ratio depends on the speed for the car you would calculate based circumferential speed of the wheel in the frame of the car (angular velocity of wheel times radius), and the actual linear speed of the car.
The reason that you get slip at even the smallest forces results not from the fact that the tire is slipping against the ground, but that the tire is elastic. Let's see how this could happen.
To measure the slip, lets put little green splotches of die on the circumference of the tire spaced 1cm apart. From this we can tell how much the wheel has rotated. Now imagine a car that is accelerating. What happens to the tires? Well the road is providing a force on the tire. What does that do to the bottom of the tire? Well just imagine a stationary tire that can't rotate and you apply a force tangent to the tire. This will cause the tire to deform and the part of the tire you are apply the force to will get scrunched up in the direction of the force. Now if you force the tire to rotate against the force, the scrunched up part will go to where the "ground" (the thing applying the force) is.
This means that our little green splotches, instead of being 1 cm apart, they will be .8 cm apart. Suppose there are a total of 11 splotches. Then by the time tire turns enough for each splotch gets to its original position, the wheel has rotated a full revolution. On the other hand, the car has only moved 8cm, because each of the splotches is .8 cm apart and there are 11 of them (so 10 intervals). Now when we compare this 8cm that the car has actually moved while the wheel rotated once to the full circumference of the wheel, which is 10 cm, we conclude that the wheel has slipped.
Since there will always be some scrunching given a non-zero tangent force, you will always get slip for a nonzero tangent force.
Of course this scrunching goes to zero in the limit of an infinitely rigid wheel, which is the sort of wheel used in physics homework problems.
Now for high enough slip ratios, the wheel will actually slide across the pavement, but until you get to the this point, static friction is still in play, so the car is accelerating from static friction.
In general, smoothing the surface, changing the interaction from sliding to rolling, adding (air) space between the surfaces, and adding lubrication (oil, graphite, teflon, ball bearings, air cushion...) are the most common techniques.
Best Answer
It doesn't matter whether the object itself is moving; what matters is whether the two surfaces involved are sliding past each other. If they are sliding past each other, the friction is kinetic; in contrast, if they are not, then the friction is static.
When a wheel rolls without slipping/skidding, the part of the wheel that touches the ground does not slide along the ground, and so the friction involved is static. In contrast, when a wheel slips/skids, the part of the wheel that touches the ground slides along the ground, and so kinetic friction is involved.
Applying the above, when a car accelerates gently, the wheels do not skid, so static friction is involved. When a car "floors it" and the wheels skid, kinetic friction is involved. When a car turns gently, without skidding/drifting, static friction is involved. When a car turns quickly enough to skid/drift, kinetic friction is involved.