# Is the main difference between the logistic regression and the perceptron the activation function they use?

I went through a Stats StackExchange's post about the difference between logistic regression and perceptron, which is too long to get the key point.

I'd like to consider the question in terms of the formulas for them.

The logistic regression is defined as

$$\hat{y} = \sigma(\mathbf{w} \cdot \mathbf{x} + b)$$

where

$$\sigma(z) = \dfrac {1}{1+e^{-z}}$$

The perceptron is defined as

$$\hat{y} = sign(\mathbf{w} \cdot \mathbf{x} + b)$$

where

$$sign(z) = \begin{cases} 1, & z \ge 0 \\ -1, & z < 0 \end{cases}$$

So, the main between the two models is the activation function, is my understanding correct?