When inquiring about the day, both of these phrases are correct grammatically speaking. In the case of the first phrase, the word “today” is acting as an adverb modifying the entire sentence. In the second phrase, the word “today” is acting as a predicative nominative and renaming the noun “day.”
A rewording of the sentences into declarative sentences can bring this into sharp focus. In the case of the declarative sentence, the word “what” has been excluded because we are no longer asking a question.
“What day is it today?” – “It is _____day today.”
“What day is today?” – “Today is ______day.”
Filling in the blanks of the two declarative sentences is easy.
“It is Monday today, not Tuesday.”
“Today is Monday, not Tuesday.”
Simply put, when you make the statement “It is Monday today.” or ask the question “What day is it today?”, you are using the word “today” as an adverb of time to describe when the action of the sentence occurs.
On the other hand, when you make the statement “Today is Monday.” or ask the question “What day is today?”, you are using the word “today” as a noun that renames the noun day.
So, as we’ve said, both are grammatically correct. Given that, which one should you use?
The answer to that is fairly simple. Whichever one you prefer! If you wish to know which one Americans would choose, the best answer we can give whichever is shorter. Americans are renowned for their efficiency!