A mirror site is a copy of the original site. Files on the mirror are served from the mirror's own local storage. Periodically the mirror site is updated by comparing the mirror site with the original site and updating the mirror wherever differences are detected. This update occurs whether it is wanted or not, and consumes storage space on the mirror server whether it is used or not. A cache site is a proxy to the original site.
Clients access the cache site which in turn accesses the original site.
Cache sites save a copy of all responses that are retrieved, so if the same file is requested more than once, the second and all subsequent copies of the file will be served from the storage on the cache site and not on the original site. A mirror site is a completely independent copy of an original site. The mirror site is updated only at fixed intervals, so content can become out of date. A cache site is a partial copy of an original site. The user of the cache has some control over the cache's expiration and update policy as well.