I use both, but I use Break Free for both cleaning and lube/protect. RemOil is mainly for lube and protection. Both seem to work well, and in fact they are the main lube products I use in smokeless firearms.
As far as I have ever heard there is only one Break Free, but it wouldn't surprise me if Winchester bought them.
Yup, a quick search found this...
The danger is not that computers will come to think like men - but that men will come to think like computers. - some guy on another forum not dedicated to machining