A state is a distinct possible situation. It can be represented as a vector that holds values necessary to recreate the current situation. The set of all possible states, regardless of whether those states can be acheived or not, is called state space.
A plan specifies a set of actions or strategies that have to be implemented to modify the state to reach the required final state under some set of constraints.
Global planning involves coming up with an overall path from the start to the end. Local planning is where we come up with immediate actions to traverse the main path.
Global planning makes use of path finding algorithms to find an optimal path from the start to the end goal. It makes use of a global costmap to find the path.
The local planner uses information about the path generated by the Global planner And a local cost map which is generated using data from the sensors to produce immediate actions that the rover is supposed to take. As the rover updates its positions we get new sensor data which is fed in to refine the local cost map.