Let's get into definitions or systems building. Mind results from the brain. Brain is like a blank template. It gets filled up with impressions (red, hot, soft, hard, like, dislike) and statements of fact. Such statements are true or false, or neither true nor false, or factoid. "A genetically modified organism is safe to eat," is an example of a statement that is neither nor false, it has no evidence in its favor or against it in the past and in the long future. A factoid is like a statement about scenes in a movie, like "Sting" where the basis of such statement is contrived. Robert Mitchum appearing in the movie, "The Longest Day" based on the Allied landing in Normandy in WWII is a factoid because Robert Mitchum was never at Normandy in the day of the landing. "Robert Mitchum appeared in the movie 'The Longest Day'" is true, But ""Robert Mitchum was in Normandy landing" is factoid.
Let's separate the brain, as matter, from the mind. (We will not resolve here the controversy whether brain and mind are the same). Brain includes its anatomy and physiology; that it is composed of fat; that it has thousands of neurons.
Mind consists of content (impressions, statements, factoid, hypothesis, predictions) and how it works (induction, deduction, logic).
Let's make a subset of mind called intellect. Intellect consists of hypothesis, predictions, attitudes, induction, deduction, and logic.
Hypothesis is a scientific guess used as guide in doing research. It consists of concepts and relationship(s) among concepts for verification. When verified as true, a hypothesis turned into theory. Prediction is a statement of fact that is unverified. In 1906, the statement E = mcsquared was a prediction. When Enrico Fermi chanced upon it in 1936 and Lise Mietner and company verified Fermi's findings in 1938 it turned into a true statement. Attitude consists of like or dislike of what is and what we would like it to be. Attitude can either be a statement or a behavior or an introversion. (There is a more appropriate term but it escapes me now). Attitude includes creativity. Logic includes mathematics.
So, mind is the whole set, intellect is a subset of mind.
An intellectual is a person who has a brain where the area that takes care of intellect is well developed.