I would say that the basic difference is this:
Grids are used as computing/storage platform.
We start talking about cloud computing when it offers services. I would almost say that cloud computing is higher-level grid. Now I know these are not definitions, but maybe it will make it more clear.
As far as application domains go, grids require users (developers mostly) to actually create services from low-level functions that grid offers. Cloud will offer complete blocks of functionality that you can use in your application.
Example (you want to create physical simulation of ball dropping from certain height):
Grid: Study how to compute physics on a computer, create appropriate code, optimize it for certain hardware, think about paralellization, set inputs send application to grid and wait for answer
Cloud: Set diameter of a ball, material from pre-set types, height from which the ball is dropping, etc and ask for results
I would say that if you created OS for grid, you would actually create cloud OS.
