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.

It should be clear that the mentioned Wikipedia page has some terminology issues.
Wikipedia's statement

A common example of a sigmoid function is the logistic function

and assertions that these functions are examples of sigmoid functions

are confusing at best.
The logistic function is not a type of sigmoid function. The sigmoid function is the logistic function. Likewise, the tanh function is not a type of sigmoid function.
Stanford's Andrew Ng states the terminology concisely in this video on neural network activation functions. This is the correct terminology to use if you are working in this field.
https://www.youtube.com/watch?v=P7_jFxTtJEo
