Why it is a range
The listed shares are not in doubt: the filings give the count and the market gives the price, so those lines are exact at each close. The doubt is in two kinds of holding. Some shares are his on paper but restricted or not yet bought, and the publishers disagree on whether to count them. And two private companies have no share price, only funding rounds and private trades, which put very different values on them.
So the low end counts only what is plainly his today, with each private company at its lower published value. The high end adds the disputed shares and each private company at its higher value. The truth, by any honest method, sits somewhere between.
What the two switches do
Turn off the 2018 Tesla shares and the options, and the high end drops to $878.1B. That is close to what a publisher that leaves them out would show. Turn them on and you have what one that counts them in full would show. Why Forbes and Bloomberg disagree goes through each choice.
How it stays up to date
The listed lines move with every US close we record on the day by day page, and with Calculate now on the home page. The share counts change only when a new filing does, and the private valuations when a new round or trade is reported, each with its date and source.