What is the difference between a reply or comment on an RT ticket?

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Responses to a ticket can be either public or private:

• Reply - a public remark that a requestor can see.

• Comment - a private note for staff not visible to the requestor. This is useful when you want to be tactful but still convey important information, like, "This student's bill was already sent to collections" or "This is a student's parent who would like to be the point of contact on any updates regarding their status." 
  Comments are only visible to the staff member with access to the queue. If you add a comment and transfer it to a different group, they will not see the comments.