Direct taxes are those levied directly on the states. If Congressed a direct tax for $435 million, California would be sent a bill for approximately $53 million, and Wyoming would get a bill for about $1 million.
Not quite. Direct taxes are not bills sent to the states, to be met as the legislature of each state sees fit. On the contrary, Congress itself determines how the tax shall be imposed and collected; in doing so, it must merely adjust the formulae used to ensure that the amount raised from each state must be proportional to its population. If necessary, it may impose different rates of taxation in different states.
For example, Congress imposed the first direct tax in 1798; one can find the text
here. The Act imposed a tax on land, property, and slaves. The rate payable in each state was equal to a national baseline rate, plus an adjustment that ensured that the state would pay a share that was actually proportional to its population (in accordance with the Constitution). The tax was to be collected by the "supervisors, inspectors and collectors of the internal revenues of the United States."
So the true difference between direct and indirect taxes is not that the federal government imposes and collects the latter, whereas the state governments impose and collect the latter on behalf of the nation. The true difference is that direct taxes are taxes upon individuals and property, whereas indirect taxes are taxes upon anything else (e.g., transactions).
