Its a stretch to use those two interchangeably. On something that isnt super tight or rusted....sometimes I grab a 13mm if I see that wrench/socket before I see the half.
Half is a TIGHT fit on some 13mm stuff and a good choice if your worried about rounding. But those two really "shouldnt" be interchanged. But several others are MUCH closer....commonly:
8mm - 5/16..........0.315" - 0.3125"..........+/- 1%
11mm - 7/16........0.433" - 0.4375"...........+/- 1%
14mm - 9/16 ........0.551 - 0.5625"..........+/-2% (this one is almost as bad as 1/2 vs 13 mm)
16mm - 5/8" .........0.630 - 0.625.......+/- 0.8%
19mm - 3/4" ...........0.748" - 0.750....+/- 0.3% (dead ringer given mfg tolerances. Im convinced they are the SAME mold just labeled differently)
22mm - 7/8............0.866 - 0.875.... +/- 1%
24mm - 15/16......0.945 - 0.9375....+/- 1%
The metric "bastards" with nothing close are 10,12,15,18.....and those are VERY common if you wrench on cars and small equip