Does comment vas-tu? and comment allez vous? both mean how are you doing?
Yes. Comment vas-tu? is used when talking with a child, close family member, or a good friend. Comment allez-vous is used to address someone you don't know well, especially an older person.
Comment allez-vous is also the plural form, when addressing more than one person.
Yes, both "Comment vas-tu?" and "Comment allez-vous?" mean "How are you doing?" in French. However, they are slightly different in terms of their usage.
"Comment vas-tu?" is an informal way of asking how someone is doing and is used when addressing a single person who you are familiar with, such as a friend or a family member. It uses the pronoun "tu", which is the informal singular form of "you".
On the other hand, "Comment allez-vous?" is a more formal way of asking how someone is doing and is used when addressing a single person who you are not familiar with, or when addressing multiple people, regardless of your familiarity with them. It uses the pronoun "vous", which is the formal singular form of "you" and also the plural form of "you".
To answer your question directly, both phrases express the same general idea of asking about someone's well-being, but the difference lies in the level of formality and the intended audience of your question.