Hi MP,
The short interest we publish is directly from the stock exchange. The data for that is collected from all the brokers in the US every two weeks and then distributed to the public, so there is a delay with this. However, in the years that I've been tracking this kind of data, we don't typically see major moves happening within a single publishing period. Typically short interest trends over the course of many weeks and months.
In regards to the shares outstanding and float - we get this information from Capital IQ. They are arguably the highest quality provider of this data around. Shares outstanding and float can change regularly, depending on a lot of factors such as if the CEO is selling, if convertible notes are converted, and so on. They track this information pretty closely and I have no reason to believe the data they provide is inaccurate. I have never heard of DilutionTracker until you mentioned it, so I cannot speak to their authoritativeness or why they might differ from Capital IQ's numbers.
In regards to free float - there is an ongoing debate about how to calculate this. Free float is the number of shares that are considered "tradable." These are all the liquid shares. Any shares that you or I or most other individuals own are liquid, since you or I can sell them at any time. Likewise, shares held by pension funds and the like are generally considered liquid and part of the free float.
However, shares that are held by company management in the form of restricted stock units are not tradable, so even though they might be counted in the shares outstanding, they are not counted in free float. Likewise, any shares that are restricted from trading after an IPO are not counted in the float.
But what about other shares held by company management? What about Mark Zuckerberg's shares of META? It's reasonable to think he might sell some of his shares, but is it reasonable to think he would sell all of his shares? It's arguable that some of his shares are not liquid, but how many?
And then there are the case of index funds. Index funds are given a mandate to track an index, which means they must mirror the positions of the index. Should the shares held by an index be counted in the free float, if they are required by mandate to hold them?
There are no hard rules for these decisions and every provider has slightly different rules for calculating float, which is why we see slightly different numbers from different providers.
One final note on accuracy - when there is a stock split in a company - then there is going to be a period where almost all share-related data is inaccurate. Capital IQ is pretty good about updating the shares outstanding right away and the float, but the stock exchanges report every two weeks, so there will be a period where the raw numbers from the exchanges are wrong. Our systems are also designed to identify and report split-adjusted figures when possible - but my advice is that if you know there is a stock split - double check your figures.