Is Wikipedia's page on the sigmoid function incorrect? Is Wikipedia's page on the sigmoid function incorrect?
It states that:

A common example of a sigmoid function is the logistic function

From my knowledge of machine learning, I thought that "the sigmoid function" is defined as the logistic function, $$\sigma(z) = \frac {1} {\left(1 + e^{-z}\right)}\text{.}$$ I have never seen or heard the phrasing that the logistic function is a type of sigmoid function.
Furthermore, that Wikipedia page says that other examples of a sigmoid function are the tanh and arctan functions. Again, I've never seen tanh nor arctan described as a type of sigmoid function.
These functions are considered to be peers, usually in a context like:
We can use various non-linear functions in this neural network, such as the sigmoid, tanh, and ReLU activation functions.
What am I missing here? Is the Wikipedia article correct or incorrect? I find that Wikipedia is usually accurate for math terms.

As Arya said, it depends who you ask, but this is not specific to Machine Learning, and even in Machine Learning the situation is not consistent (or not consistently bad). Bishop, for example, uses the term "logistic sigmoid function" and Jordan used "logistic function" already in 1995. In Statistical Mechanics, on the other hand, people are likely to call it the "Fermi-Dirac distribution/function". In some fields of biochemistry, including toxicology, you'll meet the same thing under the name "Hill equation". Etc.
It is IMHO important to remember that these are only names (words) used for describing a mathematical concept. Words is what people use to communicate, for example ideas and methods. As long as all participants of the communication understand what concept they are talking about, it doesn't really matter what words they use for it. Communities develop to a large part independently from each other (otherwise they would form a single community) and develop field-specific "dialects".
As a related example, the words "weight" and "bias", in the context of neural networks (and, through historical development, support vector machines) have completely different meanings from those used in statistics, but there is historical/field specific justification for using them.
Update: Actually, neural network pioneers commonly use "logistic function" or "logistic neuron": Hinton, Rumelhart and McClelland (also here), Sejnowski etc.
Update 2: Also, one might as well ask: "Is RBF just the Gaussian function?". For some reason, equating the two on CV doesn't seem to cause nearly as much commotion as your question.
