There are several ways to contact moderators when it is needed.
Flagging a post or comment for their attention.
Pinging them by a @moderator comment beneath the post.
Going to moderators' chat room for talking to them publicly.
Emailing them privately regarding the problem.
Question 1: Is there any difference between above options for contacting moderators depending on the seriousness of the situation? What are examples of those cases which a typical user should use one of these options but not the other because choosing a wrong option can make noise?
Question 2: What is moderators' email address in MSE?
Remark: As this question is directly related to moderators and the way that they prefer to be pinged by users, it would be very nice if we have a moderator's answer here.