The Inbox — Answering
The middle pane is the same conversation and the same composer you get at the bottom of the record page. Reply to customer reaches them the way they reached you — email if the ticket came by email, the chat window if they are still there, and both if they left an address. Internal note is never sent anywhere.
Every message carries a badge saying what actually happened: Sent to customer, Delivered in chat, Internal note · not sent, or Not delivered with the reason. An email to anyone else, a supplier say, is badged Sent to and the address, and it doesn't count as answering the customer. Press ⌘/Ctrl+Enter to send.
When a teammate has the same conversation open, the thread says so, and shows typing dots while they write, so two people stop answering one customer at once. This is for your side only; visitors never see who is viewing or typing.