These names are essentially the same concept, but at different levels of implementation:
- A pyramid is a feature of a single image, using ~33% more storage (a finite series of 25% smaller images) to capture multiple levels of resampling in a preprocessing step, so an image at a certain pixel size can be generated quickly.
- An overview is a resampled mosaic of images, preprocessing a collection of image tiles for export at targeted scales. The Image Server Extension of ArcGIS Server can serve overviews directly as an image service
- A map service cache is an image archive of pre-rendered maps, which may be just a collection of images, or a catalog or mosaic of images, or a combination of those mapping elements with additional symbolized vector data.
Performance is usually dependent on the level of effort a server must expend to respond to a request, where effort is measured in both I/O and CPU. A map service dependent on live queries from a simple catalog without pyramids would require the most effort (heavy load in both I/O and CPU), while a basemap image service can be very fast, or merely fast if it is configured to perform analysis on the fly (e.g., hillshade on a DEM overview). Map service caches generally require the least effort to serve, but only because every possible tile has been pre-rendered and stored in a compressed archive for optimal retrieval.
There are so many options because there are many ways of managing imagery, so if the execution time for using one caching technique exceeds the time between image snapshots, you can use a different technique which results in less overall work.