A question : how can I decide to buy 9.5 or 7 millimeters SSD? Where can I check the right form factor fo VAIO SZ71vn-x?
The drives ship with a plastic spacer so you should be able to adjust to fit.
To add to what Ziggy said - the Intel drive comes with a plastic spacer attached that makes the thickness 9.5mm. If your application requires a 7mm drive, just remove the four screws holding on the spacer and you now have a 7mm drive.