Well. I suppose computing with federated databases puts the emphasis on the distribution of data management resources, while cloud computing may also refer to the computational resources being supported by cloud services/infrastructure, besides the data.

Cloud computing means you have multiple options to a bundle of applications online and not getting these installed on your own machine. In case of Cloud Databases you can use any DBMS of your own choice either though Virtual Machines or Database as a Service.

But in Federated Databases you don’t need to worry about the type of database you are/will use. You just send a query to Federated Database and are automatically sent to the source thorough Federated Database Wrapper and catalog (for both local data source and remote heterogeneous database sources).

For me Cloud is a platform where a collection of applications are available to you to be used though different methods (Virtual Machines and DBMS as a Service in case of cloud databases), whereas in Grid Computing (as Federated Database is a part of it) the major focus is to share any type of resource (rather it is Data or Processing or Storage) without any information where it is being processed, stored, brought or done.