Name for grid system Is there a name for a type of grid you might find in Battleship? Where coordinates don't relate to points on a grid but rather the squares themselves?
 A: "Grid" is as good a name as any: See Regular Grid in Wikipedia: In particular, see the "related" grid: the Cartesian Grid: 

"A Cartesian grid is a special case where the elements are unit squares or unit cubes [cubes in the case of a 3-D grid], and the vertices are integer points." [brackets, bold-face mine].

You could also refer to this sort of "playing field" in a game like battleship as an incidence matrix of sorts: where a cell in the ith row and jth column might be occupied, using "$1$", or not occupied, using "$0$".
A: How about alpha-numeric grid?  That the coordinates refer to squares rather than vertices is no big deal.  Squares can be identified with vertices in the dual of the square lattice (which is also a square lattice).
A: Cell-centered grid may be a slightly better name, for when the coordinates refer to the cell. By contrast in a node-centered grid, the coordinates refer to the points on the grid. 
The distinction is important in applications such as digital image processing, computational fluid dynamics and data sets for topography and bathymetry.
