In Freshdesk, agents can converse via replies and/or public notes. Replies are standard emails, similar to the emails you send from your mailbox.
Notes, on the other hand, can be either public or private. When an agent adds a public note to a ticket, the customer does not receive the note as a separate email. They would receive a notification if the 'Agent adds comment to ticket' notification is enabled under Admin > Email Notification > Requester notification tab. Customers can view the note only if they log into the support portal and check the progress on the ticket.
A private note cannot be seen by the requester. Agents can use it to appraise each other of tickets and brainstorm on a solution to the problem. It's meant only for internal communications.