One thing about the Relion meters that I noticed (if you have a Confirm or a Micro), is that if for some reason it doesn't suck up quite enough blood, it will give you a low reading instead of an error message. When I saw a weirdly low number and suspected that the blood sample sucked in was small, I always tested immediately again afterwards twice. Sure enough, I'd find the second two numbers would be more what I expected and close to each other. This didn't happen too often, but it did happen.
I would also check and make sure the meter itself is reading correctly. If you call the company, you can get some control solution or you can test your own blood and see if the accuracy is off. It's also possible the vet's meter was off--I would ask how often they check it with control solution as well. With that big a difference, one of the meters is likely off.