And that's okay. I would much rather that if my students go to another school, they have to relearn what things are called, than if they had to relearn the techniques entirely. When we get transfer students, it's very clear very quick to me whether or not their old school did them justice. Everyone struggles learning our curriculum (like I've said in the past, a lot of rote memorization, non-standard forms, etc). But some students have sharp and clear techniques, and just need to learn our way of doing things. Others are sloppy and have no idea how to do some of the techniques we expect at their level.
If one of your students came to my school and I said "sliding roundhouse" and they did what I'd call a drag roundhouse, I wouldn't be concerned. That's something that's easy to adjust. If one of your students came to my school and had the same terminology as we do, but their technique was really sloppy, I'd have a different opinion.