Public speaking is to a general audience. Private speaking is to certain individuals.
Private speaking refers to communication that is intended for a specific individual or small group rather than the general public. It often involves personal or confidential information shared in a more intimate or discreet setting.
A conversation is two or more people speaking to each other. Public speaking is when one person stands up and makes a speech to a group of people who listen but do not normally speak until that person has finished his speech.
Public speaking requires no preparation or practice.
It depends on the context. If you are having a private conversation with someone and speaking in another language, it is generally not considered rude. However, if you are intentionally excluding others or speaking loudly in a public setting, it can be perceived as rude. Being considerate of others is key.
Public speaking indicates that you are speaking in front of a group rather than speaking that infers that you are just having a conversation. If you are talking with people that is speaking. If you are talking to people that would be public speaking.