For foundation design of water tanks, AWWA D100 specifies that water weight is to be considered a live load. I don't think that's a different approach so much as an attempt to make sure the design is more conservative than usual.
And, for elevated water tanks, AWWA D100 does not consider sloshing effects. I think there are two issues there. One is, that ground storage tanks are vertical cylinders, there's been a lot of work done on dynamic effects of that shape, and so it's easily codified. But elevated tanks are a variety of spherical/cylindrical/conical/toroidal shapes, and combinations thereof, and so it's not as easy to work with. The second thing is that on a larger ground storage tank, consideration of sloshing effects leads to a reduction in the forces, not an increase, so neglecting sloshing is conservative in those cases.