I am reading the Wikipedia article about the logistic function used in logistic regression, but I don't understand the following
A logistic function or logistic curve is a common special case of the more general sigmoid function
Why is the logistic function a special case of the sigmoid function?
I thought the logistic function was the sigmoid function. And when I look at the equation or the article it seems they are the same.
The English Wikipedia article (which admittedly has some inconsitencies) defines it as any bounded differentiable function on $\mathbb R$ with positive derivative. The German Wikipedia additionally requires that it has exactly one point of inflection. At any rate, this would allow many different functions with the typical $S$ shape and horizontal asmyptotes (the Englih one allows more wiggles than the German one, but that's details). They seem to agree that "the" sigmoidal function is the logistic, i.e. some others define sigmoidal in that narrower sense. Usually, you may not need specifically the logistic function and can work with anything S-shaped ...