I know what the difference between a public and a private reply is. 
Probably the customer doesn't know it, as all of his replies are 'public' in Freshdesk parlance.

However, once a note has been made by a customer, the tool tip for the note says Public Note.
I would recommend to change this to Note only, as it might be confusing the customer and make him think his reply is visible to anyone on the Internet.

What do you think?