You can use road tyres on turbo trainers, which I used to do many years back. The problem is that there is a lot of heat and often a lot of pressure at the contact point, so the tyre wears down a lot quicker than it would normally.
You also end up with a lot of tyre residue building up on the turbo trainer wheel, which you need to scrape off.
Turbo-trainer specific tyres are a lot harder wearing. They will last a lot longer and you won't have as much tyre residue to deal with.
One caveat is that some turbo-trainer specific tyres do have a soft layer that wears off first before exposing the harder material underneath.
As turbo-trainer specific tyres are hard-wearing it means they have very little grip and so shouldn't be used on the road.