A constant is a number, or a letter that represents a number that never changes. From the time the problem starts until as long as it lasts, its value is constant.
A variable is a letter that stands for a number that can change.
A coefficient is each of the items in a group of them that are all multiplied together.
Example: 17x + 4y
That's an expression with two terms. The terms are '17x' and '4yz'.
In the first term: '17' is the numerical coefficient. 'x' is the literal coefficient.
In the second term: '4' is the numerical coefficient. 'y' and 'z' are both literal coefficients.