I'm not sure about equivalency...
Тетрадь generally means a thin book of blank lined pages for writing notes. So it, first of all, definitely is a notebook. A tenth entry in a dictionary may say though that тетрадь can in rare instances mean any thin book whatsoever.
A copybook is largely associated with a student's exercise book containing samples of good handwriting to be copied. That would be тетрадь for as long as it is some folded paper, but more specifically it would be пропись.
One of the trickiest parts of Russian pronunciation is that only one vowel is stressed and the others have reduced sounds. Reduced vowels are like "i" in placid, "o" in political, they end up with a sounds somewhere around a short "i", "uh" or short "a". That's what's happening here, where only the а in тетради is stressed.
My students in Kazakhstan insist on using the word 'copybook' rather than notebook. According to various online sources, a copybook is not what we use in schools unless we are working on penmanship. Here is Merriam-Webster: " a book formerly used in teaching penmanship and containing models for imitation"