> where Google is getting that count
This is very likely a fairly accurate of the number of pages in Google's index that "match" the search query. Basically exactly what you would expect when you see the number.
> why the reality is so different
Cost reasons. Most search engines are more or less scanning down a sorted list of pages. The further you need to scan the more expensive it is. Just like running "OFFSET 1000" is usually slow in SQL. At some point the quality of results is generally very low and the cost is growing so it makes sense overall for Google to just cut it off to prevent it becoming an abuse vector (imagine just asking Google for the 10 millionth page of results for "cat").
The fact that few people realize that Google has a page limit shows how rarely people actually want more pages.