I assume you are talking about the coordinate system in MindPX flight stack.
Yes they do have difference.
As you can see in the picture, local position is a coordinate frame with its origin set at where the navigation system is at(point P in this picture), with 3 axis defined as N(north), E(east), Down(to earth) - NED. In practical Point P is usually set to the point that the vehicle is taking off (referred as 'home').
The global position is a coordinate frame with its origin set at the mass center of the earth. with coordinates defined in WGS84 standard.
There is also another commonly seen coordinates, the vehicle frame,
its 3-axis is also defined in NED style.
These frame coordinates can be transformed to each other.