I am new to machine learning and I am studying classification at the moment. Is it correct to say that logistic regression with more than two classes (i.e. multinomial regression) and LDA are both methods for classifying new points when having more than two classes? Or are they different things and it’s not fair to compare them? I know that in LDA we use Bayes theorem and we suppose that the distribution of the predictors is approximately normal in each of the classes and is more stable than the logistic regression model, but do they do the same thing in the end? Sorry if the question sounds silly, but I am majorly confused.
They are not the same thing. This question in various forms is asked & answered multiple times on this site, see for example Discriminant analysis vs logistic regression or Linear discriminant analysis and logistic regression and especially Why isn't Logistic Regression called Logistic Classification?. Read those posts carefully!
While logistic regression (binomial or multinomial is unimportant here) can be used for classification, that requires some extra decisions, like probability thresholds for classes.
logistic regression is not classification, it is risk estimation.
logistic regression is often more robust that LDA, since it does not use any assumption, like normal distribution, on the predictors. Such an assumption is rarely fulfilled.