This has been already discussed here. The web farm sync just creates a task for each web farm server and then, each app builds its own index files. So, the file size and file count can be different and it is by design.
Then, when it comes to different search results - I doubt that the live site app search code has 100% the same search setup - mode, condition, search options, etc. as the search preview. There are dozens of variables affecting this. Moreover, at the top of the search preview is a banner saying that it is really a basic search just to test whether there are any data indexed or not and if yes, what data are approximately in the index. You cannot put equal sign between the search preview and your live site app search.