An SEO professional asked John Mueller during a hangout about site search results and why there is a discrepancy between these and Google Search Console.
Their question was: why don’t the search results of a site query, that returns many giant numbers of results, match the indexation data that is shown in Google Search Console?
John answered that this is a question that comes up every now and then. John believes they have done a video on this separately also.
He would double check that.
Also, he thinks that what happens there is that there are slightly different optimizations that Google does for site queries in terms of: Google just wants to give you a number as quickly as possible.
This can be a very rough approximation. And this is something where when you do a site:query, this is usually not something that the average user does. So then, Google will try to give you a result as quickly as possible.
This happens at approximately the 09:35 mark in the video.