The kinematic state is defined as the position and orientation in space. The dynamic state is defined as the associated velocities.
What is the correct terminology for the combined kinematic and dynamic state? Can I call it the kinetic state?
The kinematic state involves all positions, velocities, accelerations, and orientations.
The kineto-static state involves the kinematics plus all inertial and applied forces.
The dynamic state is the integration of the kineto-static state over time.
See my answer here relating to the terminology.
Yes. Two particles at a given position, one moving and the other at rest are having the same kinematic state. But dynamic state takes in the velocity. When you need to specify both position and velocity - it becomes kinetic state. After all kinematics + dynamics = Kinetics.