Difference between interpreting linear and logistic regression coefficients

Linear regression

Let's assume, we have the following linear regression model:

Then,  the difference between two outcomes is going to be as follows:

Let's assume that x has one-unit increase, but z stays unchanged:

The difference is then as follows:

We can say that one-unit increase in x, when other parameters held constant, results in b1 increase in y.

Logistic regression

Let's assume, we have the following logistic regression model:

,

where

,

while p is the probability of an event.

The difference between outcomes is

Similarly to the linear regression case, let's assume that x has a one-unit increase, while z is held constant. Then:

We can say that one-unit increase in x, when other parameters held constant, increases the odds of the event times.
In other words, one-unit increase in x, when other parameters held constant, results in  increase in the odds of the event.

Difference

The main difference in the interpretation of coefficients in linear and logistic regression models is that in linear regression, we talk about the dependent variable (y), while in logistic regression, we talk about odds of an event.

Another difference is the way of calculating the change (using the exponent or not).