[GhostsInSnow]

I can't speak for every practice, only the ones I've worked in, however, there are general 3 options. You take home to do burial yourself or arrange with a private pet cremator, you opt for an individual cremation where they go and are cremated by the pet crematorium individual and you get the ashes back or you opt for cremation with no ashes back. This is routine cremation where they are cremated at the crematorium with all other animals that have gone for routine cremation and then are generally scatter in a remembrance garden at the crematorium.
That's how it works with us. They don't get disposed of in clinical waste or anything like that. If being dealt with by the vets, they should only ever go for cremation and should never be disposed of in any other way. We have really strict rules regarding disposal of pretty much everything even down to blood tubes and syringes etc and there are heavy fines if these aren't followed