It was Antoine Augustin Cournot who first had mentioned the number of rivals involved in competition. Competition, which once meant the way in which merchants and traders took account of how their rivals respond to their actions etc., now meant little more than the slope of the average revenue curve.
And it was Francis Ysidro Edgeworth who developed the modern idea of “perfect competition”, where the number of sellers is so great that they have no empirical affect on price. At least, this is the way it is conceived of in microeconomics textbooks.
But it was Alfred Marshall‘s “marginal utility revolution” where the use of the phrase “free competition” was much more closely related to Adam Smith’s simple system of natural liberty.
This behavioral concept of competition, which Mark Blaug calls process competition (I like this distinction), was eventually superseded by the end-state competition conception by 1933. I have no idea why Blaug chooses 1933 as the date other that it also being the darkest year of the Great Depression in the United States. (Not just in theory did everything seem “static” in those years.)
But “competition” in modern economics today is generally thought of as either perfect, where no sellers have the ability to change the price, or imperfect, the binary opposite whereby competitive performance is affected by various structures and conduct. The difference is that perfect competition does not in fact exist anywhere in observable market realities whereas imperfect competition is observable everywhere. This distinction never ceases to amuse the student of economics.