A ChunkPS Server is more commonly referred to as a Node or Chunk Node. The reasoning behind this is because each ChunkPS instance can connect to one another, either in a private network or publicly, using a custom revision system for the NBT Regions and built in Entity Tracking for servers that support it. Please Note that everything on this page is based on the current Draft, and is subject to change.
A Public Chunk Node is a node that connects to every other public Chunk Node. This set up is good for Maps that are not important (A vanilla-type Survival Map, for instance) and can be thrown away if need be. Hosting a Public Node also means that every map hosted on every other Public Node will be hosted on this one too. This is useful for a Multi-Server world setup, so you can set up cheap Server instances in multiple geological locations for people in those locations. The problem with this set up is that every Chunk Node can access your world, so if you have an important world (like a Creative or Race world), a malicious user could corrupt the map.
A Private Chunk Node is a node that doesn't access the Public Node List, and are hosted by the user or company that wants to only host their maps. A good example of this is a Creative Map, with hundreds of hours invested in it. Each Private Node can only be accessed by the person or group that set it up, so there is little chance of a malicious user corrupting your maps.
A Backup Node is a Node that doesn't have a Server Instance connected to it. These Nodes serve as fail-safes for their respective Provider Nodes, providing an up-to-date version of any Region or Chunk at any time.
A Provider Node is a Node that has a Server Instance connected to it. These Nodes provide whatever the Server needs. Provider Nodes will track regions that the Server Instance's Players are in over the idle regions, and will query a Backup Node if a newly entered region needs to be updated.
A ChunkPS Entity Tracker is basically a pass through system for servers to communicate with one another. This is extremely useful, and the core, of a Multi-Server World. This is optional and defaults to false on any Node, since the Server Instance may not choose to support it.
The Node Revision System is the heart of the Node Cloud, and such is the most complicated part of ChunkPS. The current draft of the revision system is a git-type tree, which will use the Block or Multi-Block Update Packet to keep Chunks and Regions up to date. The Revision System will also send Chunk Packets to rewrite an entire Chunk if, for instance, it becomes corrupted from a power outage or if it was regenerated.