Yes, ther are different scripits/extension suppot running for linux and windows hosting. The common one would be PHP extension for linux and ASP extension for windows. Due to the mostly more expensive of windows hosting, people is tend to choose linux hosting for nomal website without windows database support.
I don't think so. PHP is even supported in windows hosting. I have seen on many windows hosting that PHP is supported. About ASP, I'm not familiar with this extension and nor I have seen it any hosting plans.