A coefficient is a number that is constant for a given substance, body, or process under certain specified fixed conditions as to temperature, length, volume, etc., serving as a measure of one of its properties, as: the coefficient of friction, the coefficient of expansion, the temperature coefficient of resistance, etc. It is commonly used in computation as a multiplicative factor in a term of an expression.
A parameter is a measurable factor, used to identify a characteristic or a feature of a given substance, body, or process.
A "parameter" is a special kind of variable. It is a variable that either changes extremely slowly or that remains constant. "Parameter'' has several meanings:
• In physics, a parameter is a controllable quantity that physicists keep constant for one or more experiments but which they then change as desired. It usually reflects the intensity of the force that drives the system. A physical system can have more than one such parameter at a time.
• In mathematics, a parameter is an arbitrary constant in an equation, placed in such a position that changing it gives various cases of whatever the equation represents. Example: the equation of a straight line, y = c + bx. In that equation, x and y are variables; the coefficients (constants) b and c are parameters. Changing the parameters b and c gives different versions of the straight line (i.e. straight lines having different slopes and intercepts).
• In statistics, a parameter is a fixed numerical characteristic of a population. For example, the average diameter of all the apples in the world. Usually we have only a sample of a population, so in the statistics sense we have only a parameter estimate rather than a parameter's true value.
Taken from the textbook: Chaos Theory Tamed by Garnett P. Williams, US Geological Survey (Ret.), Joseph Henry Press, Washington, D.C. 1997.