http://www.mono-project.com/Main_Page
On that site, what is the difference between to two blocks to the left? They read.
Mono
An open source, cross-platform, implementation of C# and the CLR that is binary compatible with Microsoft.NET

MonoDevelop
An open Source C# and .NET development environment for Linux, Windows, and Mac OS X

Secondly, is there a way to download Mono on a Windows machine that runs in the background without also downloading the C# IDE?

One more thing. If I were to write a program on Linux with and for Mono, wouldn't that program also work on Windows & Mac providing they also had Mono installed? Thanks.

This is what i understand

Mono is an implementation
Monodevelop is an IDE(Like Visual Studio)

Mono is an alternative to the C# compiler by Microsoft(csc.exe)
It has only the command line stuff

Monodevelop is a full featured IDE

Answer to second question
If you download Monodevelop, you get Mono+Monodevelop IDE
If you download Mono, you get mono and no IDE

Answer to third question
Mono uses GTK and most of the code is portable other than platform specific ones.

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