No, both are not the same at all.
The professor is smart = الأستاذ ذكي In Arabic, this sentence is already completed because we have subject(الأستاذ) and predicate(ذكي).
The smart professor = الأستاذ الذكي.... Unfortunately, this sentence is not complete yet. That's why i put "...."
It's pretty confusing. Let me know if you don't understand. Thank you.