What is logistic about Logistic Distribution, in a common sense way? What is the lexical rationale of the name, not just pure math definition?
The distribution function is similar in form to the solution to the continuous logistic equation, giving the distribution its name.
As for the logistic equation,
The function was named in 1844–1845 by Pierre François Verhulst, who studied it in relation to population growth. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.