"Ich laufe und sie läuft."
I spoke with some native speakers about this, and basically got the impression that while "laufen" can mean walking/to walk, it usually means running, and is almost always used in that context, while "gehen" is more often used for walking. This may vary by region somewhat, but so far I haven't found any exceptions out of all the German / Swiss people I've met (though the Swiss do seem to use "ränne" for run more often, but then that's Swiss German, an entirely different beast, though it roughly correlates with "rennen").
'Laufen' means both walking and running! 'joggen' is a loan-word, from English I think. 'Rennen' can also mean a race, like 'Formel 1 Rennen' would be 'formula 1 race'!
To walk can also be 'gehen'! I think more often than not 'laufen' is used about running. And 'rennen' is mainly used about a race!(?)