When silencing a user, an automatic message is sent to that user informing them that their account is temporarily on hold. When suspending someone, I think there is an option to send an email informing them about their suspension. (Not 100% sure though).
When it comes to mute someone, it’s your choice to do so. Why should they know about that? You do not want to receive any notifications related to that user and that’s why you mute them. Imagine being a user and everyday a message is sent to you saying that someone has muted you. Would you be happy about that? No. It just causes drama.