I would think the difference between a tax and a rent is that taxes only apply to the same piece of property once and rent applies over and over.

I think that one might say that income tax taxes not money per se but income—it's, as it were, a tax on velocity (though this seems not to be quite the classic sense of "velocity of money"), on moving money rather than money at rest. Property taxes, in turn, may be viewed as taxes not on hectares (or whatever), but on hectare-years—because a hectare can't easily be valued, but a hectare-year can (comparatively). (Of course ha-yrs are not fungible, but neither are $/yr, as evidenced by different marginal tax rates at different income levels.)