Both cloud computing and mobile computing have to do with using wireless systems to transmit data. Beyond this, these two terms are quite different.
Cloud computing relates to the specific design of new technologies and services that allow data to be sent over distributed networks, through wireless connections, to a remote secure location that is usually maintained by a vendor. Cloud service providers usually serve multiple clients. They arrange access between the client's local or closed networks, and their own data storage and data backup systems. That means that the vendor can intake data that is sent to them and store it securely, while delivering services back to a client through these carefully maintained connections.