What can be used for Server to Server Web Services, SOAP or JSON. I know you can use JSON for Browser to Server, but I'm not sure if you can use it for Server to Server. One server is using Apache and the other is using IIS. Thank you.
You can use JSON for server to server. PHP for example has JSON encode and decode functions, as should any other language you may be using server-side.
You can use any format. You can think of it as an representation of your data. Json is often used when JavaScript is involved (e.g. executed by Browsers), because JSON is directly supported inside the JavaScript language.
So the format depends on your communication requirements. As you have Server to Server and different technology endpoints I would recommend the interoperable XML format.
Really any server can do the same things a client can, I don't see why it wouldn't be possible.
The application in question would have to have at least some sort of crude API at the least.
At the lowest level your server can go scrape any page and manipulate it to your liking. It wouldn't be apache doing this but your application.
JSON in sort of the lingua franca of server<=>client connections (e.g. AJAX), although I will admit a real bias toward the jQuery taconite plugin for doing AJAXy type things. Its responses are in an XML format.
Server<=>server seems to trend more toward XMLish representations. We have one project right now where there is a cluster of machines running complex simulations and they pull component parameters from a Django-based system. The access is RESTful and the responses are in XML because the other party was more comfortable with it.