These are different statements because hydrostatic pressure is being applied to the entire surface of the tank (and hence the entire surface is pushing back by Newton's $3$rd law), so the force at the bottom is not the only thing coming into play in the force balance.
The point is that the net vertical force on the water must be zero, which is distinct from requiring that the force from the tank bottom be equal to gravity. This might seem surprising, however, because we intuitively expect the tank to only need to feel the force necessary to support the water's weight- so where's the disconnect? As others have discussed, the computations are computing different things, but only the second approach yields the total force on the bottom of the tank.
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