Here I present the absolute truth of the difference between the elements Earth and Stone! True story.
It's simple, really.
The earth element is a sort of "vampire" element while the stone element is more conventional to the regular elements in the way they feed off of energy.
You see, most matoran gather their energy from other rahi through their kanohi. The earth element, however, absorbs energy from other matoran. Because of this, the earth element has been cast deep underground away from many of the others so they do not drain their food supply completely. You see, if they were allowed to roam free the casualties of matoran would drastically increase. Luckily they have adapted to conserve their power and only use it when need be in strong bursts (hence why strength is associated with their element as well).
This explains why Onu matoran do not normally show themselves in daylight (see above) and also explains why the archives existed in Metru Nui; they needed something to attract other matoran to their area. This would be perfect to lure in scholars and teachers (mostly ga and ko-matoran, however all matoran would probably visit the archives at some point such as ta-matoran making mask deliveries or le-matoran dropping off a new shipment of rahi for the archives).
Ever notice how Onua is always calm, collected and understanding? He has to be. It keeps his character approachable and generally liked. If he were, say, as hot-headed as tahu other toa and matoran might flee him and then his power levels would suffer. It's better for him to keep to the shadows and chime in where needed to help resolve conflict and keep the team unified. It's for his survival.
Other than that, though, the elements are more or less the same. You might be told something crazy like the difference deals with particle size or some other nonsense, but those are just illogical conspiracies bent on keeping the true nature of the earth element a secret as to prevent mass-panic and racism from arising through the other elements.
And that, dear friends, is the true difference between Earth and Stone.