As you can see below, the button is explicitly marked "Send a private message."

The second feature gives customers a way to send in feedback after a chat with customer support. They can rate the interaction from a disappointing 0 to an outstanding 10 and leave a comment afterward.

Twitter has always been very welcoming of brands that want to use its platform for customer care. It even published a guidebook for businesses last year. While these tools won't have a huge effect on the way you tweet, they might prove to be useful down the line when you need to reach out to a company.