[c#] What’s the difference between Response.Write() andResponse.Output.Write()?

Nothing, they are synonymous (Response.Write is simply a shorter way to express the act of writing to the response output).

If you are curious, the implementation of HttpResponse.Write looks like this:

public void Write(string s)
{
    this._writer.Write(s);
}

And the implementation of HttpResponse.Output is this:

public TextWriter Output
{
    get
    {
        return this._writer;
    }
}

So as you can see, Response.Write and Response.Output.Write are truly synonymous expressions.