Self Hosted: An application (usually running on a server) that you run in your own environment.
[Note, Self Hosted services may still be classed as self-hosted, even if you don’t manage the environment yourself, for example, if you use a Virtual Machine, a Virtual Private Server, or pay someone like modular.im to build and run it for you – provided you can migrate your hosted application to your own environment if you want to]
P2P (Peer to Peer): A locally running application (or client) which predominantly talks to other clients (referred to as a peer), not to a server. There may be a central server which helps facilitate the initial connection between applications, but this is typically only used for that introduction. There may also be a semi-fixed list of “seed nodes” used to discover other nodes in the network.
Examples include: Bittorrent, Secure Scuttlebutt
[Many VoIP systems will have some sort of federated connection between “signalling” nodes, but have a P2P connection for the Audio/Visual streams.]
Federated: A server-based application that can talk to other server applications. (Federation can also refer to the method by which they find each other – either by responses to specific HTTP(s) requests or from particular DNS records).
Examples include: Matrix.org, Mastodon
Distributed: This is more how data is processed – if it’s centralised but distributed (e.g. Facebook, Netflix) then a central server instructs other servers how to act, and the nodes perform actions on behalf of the server. When talking about Decentralised, this means that you could have several nodes cooperating on an activity.
Examples include: BOINC, DNS
Blockchain: A distributed, secure, append-only database. May be P2P or Federated.
Examples include: Bitcoin
Decentralised: Any application which does not require a central service to function. Usually implies Self hosted.Enhanced from a message sent to the #redentralize:matrix.org chat, following advice from participants in the group
Examples include: Collabora Online, “Internet Mail” (the original decentralised service!)
I hope you find this list of definitions useful!
(Edited 2019-02-21 to address comments from Ben in the Binary Times Telegram group, also others from mylo5ha5 in the Redecentralize group. Typo fixed, thanks to uhoreg)