What are the outputs of the logistic model and the logistic function?

The logistic model outputs the logits, i.e. log odds; and the logistic function outputs the probabilities.

Logistic model =

$\beta_{0} + \beta_{1} X_{1} + \beta_{2} X_{2} + \beta_{3} X_{3} + ... + + \beta_{k} X_{k}$

The output of the same will be logits.

Logistic function=f(z)=1(1+e−(β0+β1X1+β2X2+β3X3+...+βnXn))

$f(z) = \frac{1}{(1 + e^{-(\beta_{0} + \beta_{1} X_{1} + \beta_{2} X_{2} + \beta_{3} X_{3} + ... + + \beta_{k} X_{k})})}$

The output, in this case, will be the probabilities