TLDR these are different counters and measure different things - the FujiFilm numbers are likely more reliable for actual shutter counts.
The technical reason why your result using the web site is so much lower is that the field holding the counter is only capable of holding numbers up to 64K (and to compound that the web site misreads the number and rolls over at 32K). The bottom line is that this web site will never show numbers over 32K with a FujiFilm camera.
You also have to be aware that the metadata number is incremented using both the mechanical and electronic shutter and, when you use preshot, the number includes images stored in the buffer and never actually written to the card.
There are situations when the counter can be reset (such as the internal battery losing power) but thats probably not the reason your numbers are different.