There are actually four ways that are commonly used to attach a car seat cover.
The first is elastic, and while this works great it can also wear out over time. Secondly is a strap/buckle combination. This is our favorite because it will last. Third is a zipper compression fit. Lastly, some brands are using hooks. That’s a similar approach to a strap/buckle so it’s pretty good as well.
In addition to these common ways to secure a seat cover, lots of brands add “no-slip” backings to their covers. Which is usually some texture to help prevent it from moving around.