Both oxides have several polymorphs. If you need the corundum structure, then M is at [0; 0; 0.3522] and O at [0.3063; 0; 0.25]. You can find other possible structures at http://www.crystallography.net/
Please use the terms correctly: Fe2O3 is a structure, and since Fe and Al are different atomes the coordinates are perhaps not identical (but this also happens for different Fe2O3 description :-)). Again: main message: Don't mix lattices with structure. Only because all around you do it it doesn't mean it is correct. :-)
Of course you do, but why do you use it then in the wrong way? Here are many readers who do not diistinguish between both terms and don't see any difference.