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.