It's completely different.
On Linux, Blender allocated memory successfully. Then it tried to use it, and the OOM killed it => work is lost without notice.
On Windows, Blender tried to allocate memory, but it failed. A good software should always recover gracefully after a memory allocation failure: in this case, Blender can save the work done, and gracefully exit; or stop the current task, or something like that.
It's true that some programs don't behave well when in an out of memory condition, but the OS should leave a chance to the program to continue its operation, instead of killing it when it shoud never have happened.
Of course, this is in the case the OOM decides to kill the process you're using. But when it decides to kill X, you lose all your unsaved work. That should never happen.
And don't get me started on the OOM killer in a server environment... Yeah, good idea to kill apache or MySQL on a web server.