It depends on how many riding definitions you are 'recognising'
If the only riding sub genres are Cross Country and Downhill/Freeride (plus BMX, road, CX, DJ etc etc) then Cross Country would seem* to be anything that involves riding up hills on an 'MTB'
If you 'recognice' many other marketing sub genres and it breaks down something like: XC, Trail, All mountain, Freeride, Downhill (+ others mentioned previously) then in that order it seems to correalate to how well the bike will go up and downhill
then XC would seem* to include XC racing, XC endurance racing, trail centre/'natural' trails that don't include any/many (bigger) 'technical trail features'/jumps/drops/'northshore'/etc ..
All mountain I thought was supposed to be bikes that will ride up pretty much any mountain uphill and down pretty much any mountain downhill. In practice it seems to used on bikes that will just about winch up a fireroad and handle the downhills much much better than the ups
Trail would seem* to be some kind of middle ground between XC and all mountain and freeride and downhill, basically XC trails with (some/more) 'technical trail features' and (some/more) bigger jumps/drops/'northshore'/etc ..
*this is just my interpretation of many different 'definitions' and sub genres