Logistic or Logit or doesn't matter

Stata do file

* I was recently attending a talk in which the presenter talked about logit in contrast with logistic regression when the outcome variable was binary saying logistic was similar.

* This confused me.

* Looking at the equations for logit vs that of logistic I think it is clear that a logit regression is a special case of a logistic regression.

* However, in case there is still doubt.

clear
set obs 100

gen x = rnormal()
* Some explanatory variable

gen y = rbinomial(1, normal(x))
* Some binary response variable

mlogit y x, baseoutcome(0)

logit y x
* We can see the estimates are identical.