In my limited understanding it's the difference between the webkit engine that OS X provides to developers to use, as opposed to Chrome which probably does something different in that regard. Besides site-specific browsers, there are plenty of makeshift OS X tools that implement their own built in browser, and these applications do indeed share cookies with Safari.
The easiest way to test this is with Safari and any of the OS X site-specific browser or http debugging tools.
The easiest way to test this is with Safari and any of the OS X site-specific browser or http debugging tools.