Some online shops make an effort to validate vision prescriptions, others do not. My most recent contact order was through Lens Direct, who did not validate. 12 years ago I gave an incorrect phone number for the optometrist. They tried to call but did not connect, and sent me an email: 'we're going to send your contacts anyways...'
The optometrist I went to recently put me in the strongest prescription I'd ever had. Instead of using that prescription, I ordered contacts using the prescription of the glasses that I thought were fine.
There's two numbers on the contacts... diameter of the pupil (doesn't matter for most people I think) and an angle (Edit: 'Base Curve'. The third number is the power of the contact, aka 'sphere'. Glasses prescriptions have power and astigmatism, but don't have diameter or base curve). I got these off my prescription. If you don't already know how to use contacts it's important to get instructions and a followup. I read of a guy who didn't know he had to take the contacts out at night - the contacts had started to grow into his eyes?
(Edit: you can get a set of "trial lenses" from Ebay if you want to try to come up with your own prescription, or to try out your prescription before buying glasses.)
My previous comments on ordering contacts:
https://news.ycombinator.com/item?id=13691768 / https://news.ycombinator.com/item?id=29366816
Edit: I live in the United States.