Logit and logistic regression are the same thing. However, they actually relate to generalized linear models. In a generalized linear model, you have some features , parameters , response , and link function . that relates to and . The relationship is as follows:
One choice of is the logit function . Its inverse, which is an activation function, is the logistic function . Thus logit regression is simply the GLM when describing it in terms of its link function, and logistic regression describes the GLM in terms of its activation function.