Think of as conveyor belt, initially at rest. There are things on it, also in rest. The belt gets moving, and the things on it will move together with the belt. They must have been accelerated, what was the force?
so when we consider the friction between the belt and the 'thing', it's static friction?
and when we consider the friction b/w ground and 'thing', it is kinetic friction?
If the object does not move with respect to the belt: it is static friction between the belt and the object. It opposes the motion relative to the belt and makes the object move with respect to the ground.
There is no interaction between the ground and the object on the belt (except gravity). Friction is a contact force.
A car accelerating on level ground is an interesting example. The force accelerating the car (but NOT the energy it acquires) is from the road. The force involved is static friction between the road and the tyres. If the tyres slip on the road the car doesn't accelerate. So although the force opposes relative motion between the bottom of the tyre and the road, by doing so the force accelerates the car! [I've sometimes thought that there were two brilliant discoveries/inventions concerning the wheel. The first was that fitting wheels to a cart, chariot etc. enabled it to be dragged with little resistance, the second was that turning the wheel moved the cart forward.]