It's most definitely not stored in real-world units, it's still stored in user units, it's just trickier to find out what they are. If I read the SVG specification they should be in pixels (which is a unit that's coupled to the viewing device).
We usually call these "SVG pixels". Any anonymous units in SVG are supposed to be SVG pixels. Their relation to absolute units must be dependent on resolution, but Inkscape has it hard-coded as 1 SVG pixel equals 0.8 pt. Testing shows that Adobe SVG plugin uses the same value, while Batik has a slightly different coefficient (see https://sourceforge.net/tracker/index.php?func=detail&aid=964481&gro...) at least on my machine. I don't know if Batik or Adobe really change that coefficient depending on screen resolution (but I doubt that).
It is my opinion that introducing resolution-dependent units into SVG and especially allowing them to mix with absolute units was a very bad idea. One way to mitigate the consequences is to try to always use only pixels or only absolute units. This is what we do; we convert all lengths to SVG pixels internally and write them as anonymous SVG pixels on save. If you're interested in absolute units, just consider the SVG pixels as yet another absolute unit with the fixed 0.8 coefficient to points.