structure-wise, they are not the same actually.
When you use the verb (to be) in a sentence, like "the professor IS smart" you are telling a fact. In this instance, the adjective "smart" is predicative (i.e. used to tell something).
However, in the phrase (the smart professor), we are dealing with a noun and its adjective (adjectives in Arabic come after the noun and mimics its status). In this instance, the adjective is called "Attributive," that is something attached to the professor himself. We are not about telling something here, we are simply stating the professor as it is and attaching an adjective to it, and the sentence is yet to be completed by other elements to understand the whole meaning.
Pretty sure the suggested English translation is not correct under uk usage, it may be different under US usage. The phrasing in UK english is different if you have a different noun/adjective. If for instance it was french, you would get the professor is french, but because arab starts with an a you would get the professor is an arab, or the professor is arabic.