In a .csproj file, what is <None Include="..."> for?

The MSDN article on the build action property explains the differences.

None - The file is not included in the project output group and is not compiled in the build process. An example is a text file that contains documentation, such as a Readme file.

Content - The file is not compiled, but is included in the Content output group. For example, this setting is the default value for an .htm or other kind of Web file.

One difference is how they get published; "None" items don't get included in a publish, "Content" items do; for example, on the "Application Files" dialog on the Publish tab.