I have read about a common fraction in this statement (written in a text book):
Ratio is the simplest form of a common fraction, in which the numerator denotes the antecedent and the denominator denotes the consequent.
The Wordweb dictionary defines a common fraction as
The quotient (defined as "The ratio of two quantities to be divided" / "The number obtained by division") of two integers.
From this definition, a common fraction pretty much seems to be just the same as a fraction. So what is the difference?
Though I doubt there is any authoritative definition, I've always taken common fraction to mean a ratio of two integers, whereas a fraction is a ratio of any two things. For example $$\frac{1}{2},\qquad\frac{17}{2^4},\qquad\frac{12}{24},$$ are common fractions, whereas $$\frac{\pi^2}{6},\qquad\frac{1}{\sqrt{2}},\qquad\frac{x^2+3}{x^3-1},$$ are fractions, but not common fractions.