1. A content providing and obtaining system composed of a content providing apparatus for providing compressed content data generated by compressively coding content data by a specified compression coding method, and a content obtaining apparatus applying a specified decoding method corresponding to the specified compression coding method, for obtaining said compressed content data provided from said content providing apparatus, wherein: said content providing-apparatus: stores on the content providing apparatus said compressed content data compressively coded by at least one kind of compression coding method, receives identification information for identifying said specified decoding method applied to the content obtaining apparatus, and specifying information representing specified content data, transmitted from said content obtaining apparatus, in response to receiving the identification information, detects whether or not specified compressed content data generated by compressively coding said specified content data by said specified compression coding method corresponding to said identification information has been stored thereon according to said identification information and said specifying information, to generate a detection result, in response to determining that the detection result indicates that said specified compressed content has been stored, reads said specified compressed content data or in response to determining that the detection result indicates that said specified compressed content data has not been stored, compressively codes said specified content data to generate said specified compressed content data, said specified content data being original data of the specified compressed content data before being compressively codes by said specified compression coding method, and transmits said specified compressed content data to said content obtaining apparatus; and said content obtaining apparatus: transmits said identification information and said specifying information to said content providing apparatus, receives said specified compressed content data transmitted from said content providing apparatus, and decodes said specified compressed content data by said specified decoding method, and generating said specified content data.