Open Source = source is available and free as in beer. Examples: libpng, zlib, apache, python, llvm, chrome, firefox
Free Software = source is available and free as in beer and copylefted (you must also release your derivatives as free software). Examples: gcc, mysql, linux, gnome, gimp
Unreal is neither of these. It's not free as in beer nor copylefted. It's just that if you are allowed to use the source if you license the engine.
Open source software does not necessitate any price requirements, but rights to redistribution, modification and running for any purpose without restriction. The definition you gave - "source is available and free as in beer" can still very well apply to proprietary software, if redistribution is forbidden. There actually is such a thing, it's called "shared source" by Microsoft.
Free software is any software that satisfies the four essential freedoms [1], of which being copyleft is absolutely not required in any way.
For all practical purposes, OSI and FSF standards are equivalent. They differ in that the former is more oriented toward pragmatics and business, whereas the latter toward ethics and philosophy. As a result, the FSF tends to encourage copyleft more than the OSI do, but they do not necessitate it by any means.
Free Software = source is available and free as in beer and copylefted (you must also release your derivatives as free software). Examples: gcc, mysql, linux, gnome, gimp
Unreal is neither of these. It's not free as in beer nor copylefted. It's just that if you are allowed to use the source if you license the engine.