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Wiki:

Cloud computing refers to computing resources being accessed which are typically owned and operated by a third-party provider on a consolidated basis in Data Center locations. Consumers of cloud computing services purchase computing capacity on-demand and are not concerned with the underlying technologies used to achieve the increase in server capability.
The applications of cloud/utility computing models are expanding rapidly as connectivity costs fall, and as computing hardware becomes more efficient at operating at scale. The economic incentives to share hardware among multiple users are increasing; the drawbacks in performance and interactive response that used to discourage remote and distributed computing solutions are being greatly reduced.

Grid computing is a term for either of two broad subcategories of distributed computing:

• Online computation or storage offered as a service supported by a pool of distributed computing resources, also known as utility computing, on-demand computing, or cloud computing. Data grids provide controlled sharing and management of large amounts of distributed data, often used in combination with computational grids.

• The creation of a "virtual supercomputer" composed of a network of loosely-coupled computers, acting in concert to perform very large tasks. This technology has been applied to computationally-intensive scientific, mathematical, and academic problems through volunteer computing, and it is used in commercial enterprises for such diverse applications as drug discovery, economic forecasting, seismic analysis, and back-office data processing in support of e-commerce and web services.

A server farm or server cluster is a collection of computer servers usually maintained by an enterprise to accomplish server needs far beyond the capability of one machine. Often, server farms will have both a primary and a backup server allocated to a single task, so that in the event of the failure of the primary server, a backup server will take over the primary server's function.
Server farms are typically co-located with the network switches and/or routers which enable communication between the different parts of the cluster and the users of the cluster.
Server farms are commonly used for cluster computing. Many modern supercomputers comprise giant server farms of high-speed processors connected by either Gigabit Ethernet or custom interconnects such as Infiniband or Myrinet.

So there it is. Grid computing can have both of these. And yea, grid computing formation and study has a LOT of mathematics and theories involved, complicated stuff!