Difference among these three

What is the difference amount these three:

  1. Participation Node
  2. Relay Node and Private Network
    Is is possible to run a node with windows?

A description of participation nodes and relay nodes is provided on https://algorand.foundation/network

Note that a participation node can in theory be a relay but this is highly discouraged for security reasons.

The notion of private networks is orthogonal to the notion of nodes. For details about networks, see https://developer.algorand.org/docs/networks

I don’t think Windows is officially supported. However, you can definitely run a node using Windows Subsystem for Linux (WSL) with Ubuntu 18.04.

You may try this Algorand Docker Sandbox too: