A Grid is a hardware and software infrastructure that clusters and integrates high-end computers, networks, databases, and scientific instruments from multiple sources to form a virtual supercomputer on which users can work collaboratively within virtual organisations
Grid is Mostly free used by academic research etc.
Clouds are a large pool of easily usable and accessible virtualized resources (such as hardware, development platforms and/or services). These resources can be dynamically reconfigured to adjust to a variable load (scale), allowing also for an optimum resource utilization. This pool of resources is typically exploited by a pay peruse model in which guarantees are offered by the Infrastructure Provider by customized service level agreements.
Cloud is not free. It is a service, provided by different service providers and they charge according to your work done.