On the one hand I have seen, in the HoTT book for example, precategory and category being used where the latter has the map idtoiso being an equivalence.

On the other hand I have seen people call these categories and univalent categories which is also fine.

Now because we have Rezk completion every precategory is yearning to become a category, so some might argue that a distinction isn't necessery. I would argue that the HoTT book convention is infact more misleading as "precategory" there is really just the usual notion of category. And a univalent category is some nice structure we can add to it because we are working in HoTT.

What are your thoughts and opinions on this?